# Oral-History:Manfred Schroeder

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− '''Schroeder:'''
Well, before being accepted into an institute to do your Master’s thesis, at that time—it's no longer the case—you had to build up some new laboratory experiment. In those years there was no institute at Göttingen with equipment for experimenting with microwaves. I was supposed to build the first laboratory experiment involving microwaves in hollow metal tubes. We had some magnetrons and klystrons and round waveguides. I said to Professor Meyer, "Round wave guides, that means Bessel functions." If there's one thing I don't like—I always had strong dislikes—it's Bessel functions. Meyer replied, "The only thing you have to know about Bessel functions is 1.84 and 2.40. One is the first zero of J0 and the other is the first maximum of J1." This was basically true. You didn't have to know much about Bessel functions. + '''Schroeder:'''
Well, before being accepted into an institute to do your Master’s thesis, at that time—it's no longer the case—you had to build up some new laboratory experiment. In those years there was no institute at Göttingen with equipment for experimenting with microwaves. I was supposed to build the first laboratory experiment involving microwaves in hollow metal tubes. We had some magnetrons and klystrons and round [[Waveguides|waveguides]]. I said to Professor Meyer, "Round wave guides, that means Bessel functions." If there's one thing I don't like—I always had strong dislikes—it's Bessel functions. Meyer replied, "The only thing you have to know about Bessel functions is 1.84 and 2.40. One is the first zero of J0 and the other is the first maximum of J1." This was basically true. You didn't have to know much about Bessel functions.

## About Manfred Schroeder

Dr. Manfred R. Schroeder was born in 1926 in Germany, where he grew up during Adolf Hitler's regime. Schroeder's early interest in science and mathematics led to experiments with radio sets and shaped his later military service during World War II. He learned to work with radar systems during service with an anti-aircraft battery in Poland and with the navy in Holland. After the war, Schroeder returned to Germany and began his higher education in electrical engineering. He received his Vordiplom in mathematics and his Ph.D. in physics from the University of Goettingen in 1951 and 1954, respectively. In 1954 he went to work for Bell Labs, where he researched microwave and acoustic relationships and focused on speech acoustics. Schroeder built speech synthesizers, experimented with bandwidth compression and adaptive predictive coding of speech for telephone communications systems. In 1963 he became Bell Labs' Director of Acoustics and Speech Research, and in 1969 he accepted a full professorship in physics at the University of Goettingen, where he spent half his time and shared the other half with Bell Labs. Schroeder has contributed much to improving the acoustics of major concert halls worldwide, as well as improving the audio qualities of the telephone system. He is a Fellow of the IEEE and a member of many other professional and honorial societies, including the Max Planck Society, the Acoustical Society of America, the Academy of Sciences at Goettingen, the National Academy of Engineering, and the New York Academy of Sciences.

The interview discusses Dr. Schroeder's education and his professional career, focusing on his experiences during WWII as well as his later years spent in academe and research. Schroeder discusses his work with radar during the war and explains how this shaped his subsequent electrical engineering career. He describes his years with Bell Labs, especially his work with concert hall acoustics, speech synthesizers, bandwidth compression, and the development of a vocoder system. Schroeder recalls his decision to join the faculty at the University of Goettingen and his work with the students there. The interview concludes with his explanation of how to design modern concert hall ceilings which maximize acoustic quality.

## About the Interview

MANFRED SCHROEDER: An Interview Conducted by Frederik Nebeker, IEEE History Center, 2 August 1994

Interview # 217 for the IEEE History Center, The Institute of Electrical and Electronics Engineers, Inc., and Rutgers, The State University of New Jersey

This manuscript is being made available for research purposes only. All literary rights in the manuscript, including the right to publish, are reserved to the IEEE History Center. No part of the manuscript may be quoted for publication without the written permission of the Director of IEEE History Center.

Request for permission to quote for publication should be addressed to the IEEE History Center Oral History Program, Rutgers - the State University, 39 Union Street, New Brunswick, NJ 08901-8538 USA. It should include identification of the specific passages to be quoted, anticipated use of the passages, and identification of the user.

It is recommended that this oral history be cited as follows:
Manfred Schroeder, an oral history conducted in 1994 by Frederik Nebeker, IEEE History Center, Rutgers University, New Brunswick, NJ, USA.

## Interview

### Germany in the 1930s and 1940s

#### Family background and youth

Nebeker:
You were born in Germany in 1926?

Schroeder:
Yes, in a city called Ahlen in what is now the state of North Rhine-Westphalia (Nordheim-Westfalen).

Nebeker:
What did your parents do?

Schroeder:
My father was a mining engineer and my mother was a housewife.

Nebeker:
You must have been six years old when Hitler came to power.

Schroeder:
That's right.

Nebeker:
How did the Nazi regime in the pre war period affect you and your family?

Schroeder:
It affected us in a number of ways. Of course, I remember the early days of the Third Reich only dimly. I do remember, however, when I was seven, in 1934, that Ernst Röhm, one of Hitler's closest associates, was arrested and shot. As a child, I was surprised and thought, "Well, wasn't he Hitler's best friend? And now suddenly he is dead." That's one of my earliest memories. So I thought something was fishy.

My father had been a combat pilot in World War I and always liked flying. Between the wars he founded a private flying club. Even my grandfather had to join; he never actually flew, but he was a paying member. The family was taken up in planes and so forth. Then in 1935 when a German Air Force, the Luftwaffe, was reestablished, my father joined. He became a professional Air Force officer, eager to fly again. But by then he was over 40, and he never actually flew a combat plane again. This all was a great disappointment for him, and in July 1944 he was discharged from the Air Force. He was only 51 and in perfect health, but he was discharged. The Nazis had become distrustful of the “older” officers.

Nebeker:
He didn't fly in combat during the war?

Schroeder:
No. He was too old. After he was discharged he went back as an engineer to private industry (Telefunken, where ceramic triodes for cm-radar were developed).

Nebeker:
Were you interested in science from an early age?

Schroeder:
Yes. I remember the boys from the street always rang the doorbell. They were playing soccer or Schlagball (softball) on the street and asked me to join them. I was sitting in my room doing mathematics, even when I was eight or nine years old. So my mother would say, "Manfred cannot come. He is pulling little roots." That was her expression, her metaphor for mathematics. She knew about square roots, so she said, "He's pulling little roots," and the boys went away. However, whenever a good practical joke was in the offing, I would drop everything to join the “gang”. I've never become, to this day, much interested in any sport, including soccer or baseball or basketball. I have, however, played tennis, I am still an avid skier, and I have sailed with Max and Marj Matthews in Greece, the Caribbean and along the Eastern Seaboard. I also loved ice skating—including helping “fallen” girls back on their feet.

Nebeker:
Were you more interested in mathematics than in gadgets?

#### Building a radio transmitter, secretly listening to foreign broadcasts

Schroeder:
Yes, that's right, that's a good point. I did build a model plane or two, and, oh yes, I built a little radio transmitter. It was completely self contained with batteries, and I built it to be placed in the teachers' conference room. My parents were scared to death. This was in the middle of the Nazi period. I would go a mile or so away to a friend's house to listen to my transmitter. Then when something didn't work, I came back and knocked on the door. My parents thought it was the Gestapo. No, it was only me checking on something.

I remember on another occasion I was operating my secret transmitter, and I saw the Wehrmacht (Army), or maybe it was the SS (Schutzstaffel), with direction finding equipment outside the house. I turned the transmitter off and didn't turn it on for another month. They were obviously looking for me, and in those days that was not a joking matter.

Nebeker:
It was against the law to operate a transmitter?

Schroeder:
First of all, it was against the law. Also, in those days and during the war, one could easily be accused of being a spy and of conspiring against Hitler. It was very, very dangerous. I was also always listening to the BBC (British Broadcasting Corporation) from London, because somehow I felt I got better information from them than from the German stations.

Nebeker:
Were these the German language BBC broadcasts?

Schroeder:
I'm not quite sure in retrospect. Even today I never know whether I'm speaking German or English.

Nebeker:
You learned English at an early age?

Schroeder:
Yes, but probably it was German. But on occasion I must have listened to English language transmissions, because I remember I was in a hospital on June 6th 1944 and at three p.m., after my midday nap, my ear very close to the loudspeaker—again it was forbidden to listen to the American Forces Network broadcasting from London—I heard the words that I still remember: "This is the American Forces Network (AFN) and the Army Air Force Band under Major Glenn Miller. Hello, boys in France." Then they played "American Patrol." I still remember that. And I was wondering how many Americans on the Normandy Beaches were listening: "Hello, boys in France."

Nebeker:
Was that a small crystal receiver you were listening to?

Schroeder:
No, but it was a very small receiver. My nightstand had two levels. It fitted between the two levels and was right next to my ear. This was important, because I always feared that if somebody heard that I was listening to the BBC or the AFN it might cause trouble. That's an understatement, because many people went to concentration camps for listening to foreign stations and then, deliberately or otherwise, spreading the news.

Nebeker:
The radios that were manufactured in the Third Reich, could they pick up the BBC stations?

Schroeder:
That's a very good question. The so called People's Radio (Volksempfänger) was deliberately constructed to be able to receive only the nearby German stations. But you could buy super heterodyne receivers, big ones, able to receive stations from many countries. I remember I listened to stations in Czechoslovakia in 1938 before the Germans took over and to many other foreign stations. I remember listening to a station from the U.S., which I thought was "Shen ek TA dee"—on our dial appeared the word "Schenectady"—and it wasn’t until 20 years later that I discovered it was "Ske NEK ta dee."

So there must have been very small super heterodyne receivers, or I wouldn't have been able to receive London from this hospital room. But the government intention was of course to supply the population at large with cheap receivers that could only get the local stations whose programs were of course controlled by Goebbels.

Nebeker:
This transmitter that you built, how large was it?

Schroeder:
About one by one-half by one-half foot. The bottom size was dictated by the battery, a 120 volt battery that was this size. Then for the heaters, it had two lead acid batteries on top. I had a very good microphone. It did the job well.

Nebeker:
Did you place it anywhere else besides the teachers' conference room?

Schroeder:
No, I didn't.

Nebeker:
You weren't a ham radio operator?

Schroeder:
Not really. As I said I was interested only in mathematics and not gadgets, but I did build this working transmitter for voice. To become a licensed ham operator in Germany then was very difficult. Even today in democratic Germany to get an amateur license is a major undertaking (as are so many other things that are easy in the States). I never tried. Of course I was quite young too. I remember the principal of the school, who also taught us mathematics, said, "Don't waste your time becoming a ham operator. Do basic physics and mathematics." I took his advice. During the war, after I had been drafted, this principal and I corresponded about certain mathematical problems, like the indeterminate integral over exp(x)/x, which I couldn’t solve.

I did become interested in ham radio for the following reason. At the beginning of World War II a friend of mine could read Morse code, and I was very much impressed by his listening on shortwave to transmissions from around the world. I wanted to be able to do that too, so I got a book on Morse code. After a week or two, though, I gave up. Then I got a book on how to build your own transmitter, which I found was way over my head. So I got some basic books on electrical engineering, and I studied those. Finally I was able to build that transmitter.

#### Education

Nebeker:
Were your school days challenging for you in the math and science that was taught?

Schroeder:
No. I was always ahead of the class and occasionally ahead of the teacher. I recently met with an old friend, Jobst von Behr, from the early 1940s, and he reminded me that at one point our physics and mathematics teacher wanted to explain the Doppler effect to the class. Okay, as the source comes toward you the frequency is higher and then it drops. Then he wanted to explain the Doppler effect if the source doesn't move directly toward you but passes you by. He got stuck. I had heard of the Doppler effect before when our radar was converted to Doppler after the disastrous firebombing of Hamburg in July 1943. Of the thousands of bombers only 17 where shot down because the Allies were using chaff (Düppelstreifen in German) for the first time. In any case, I immediately grasped how the Doppler effect worked. I explained the whole thing to the teacher and the (amused) class. It's really quite simple: a bit of Pythagoras and differentiating a square root.

Nebeker:
In 1939 you turned 13. How did the war affect your schooling?

Schroeder:
I would say not at all. I was a commuting student from a small town in the Lüneburg Heath. There were no good schools there, no high school really, so I had to commute to the city of Bremen. In the beginning of the war there was hardly any change. Some teachers must have been drafted, though I don't remember that.

Nebeker:
Your teachers were mainly men?

Schroeder:
I don't think there were any women teachers. In this school I was not only very good in various subjects, including languages, but I must have made some kind of exemplary impression. For when we left the Bremen area in 1940, the director of the school spontaneously wrote a letter to my father—I wish it still existed—regretting that of all the pupils, the best—and he didn't mean just academically, but in setting an example and so forth—was leaving the school.

I recently revisited the school. I told the building superintendent that I had been there 50 years ago, and she said, "Well, go and see the director. He is in." I mentioned the story that I just told you, and you wouldn't believe it, he talked to a secretary, and ten minutes later she came back with my complete records. Not a copy of that letter, alas, but he could tell from the records that I had been an outstanding student. I was flabbergasted. He made Xerox copies for me.

Nebeker:
Where did your family go in 1940?

Schroeder:
My father, as I said, was an Air Force officer, and he was working at a supply center (Luftzeugamt), an air base where new fighter planes were tested and huge stores were kept. This was a very large installation, and of course they were afraid of British bombers. They built a sham airport about five miles away, another big operation. You can't simulate a big operation with a small one. You wouldn't believe it, but the British dropped wooden bombs on the sham airport. This, of course, was a mistake, because then the Germans got the message and shut down the sham airport at a saving of millions and concentrated on defending the real thing.

One means of defense was to move the Luftzeugamt far away to Liegnitz in eastern Germany, Silesia. So my father in late 1939 or early 1940 was transferred to Silesia, leaving the family behind. The family had often been separated, but my mother said, "Not again." So we moved to Silesia too and stayed there the rest of the war (until the Russians came). There was enough food and there were no air attacks.

Of course I had to change schools. The letter that I mentioned must have gone to my head, because at this new school I became the worst pupil. Academically I was still very good, but I gained a very bad reputation. For example, I didn't like drawing. I revisited that art room two or three years ago. It is now in Poland. The drawing class was always two hours, and during intermission the teacher would go to the teachers' room. I would sit there with my dirty water from washing the brushes and wait for the teacher to exit the door three or four floors below and then dump it on him. This time the teacher never appeared, but suddenly there was a hand on my shoulder. The teacher was behind me. That was one incident; there were many of that sort. So when I switched schools again, they didn't write to my parents, but the director told me, "We are happy you are leaving."

Nebeker:
Did you go to Gymnasium there?

Schroeder:
Yes. First in Ahlen, where it was actually called Gymnasium. In Bremen it was called an Oberschule, which probably meant that one started with English rather than Latin, but otherwise they were basically the same.

Nebeker:
I see. You concentrated on math and physics?

Schroeder:
Well, there were no electives in those years. Everybody took the same courses.

Nebeker:
There must have been a math line and a language line.

Schroeder:
No, none whatsoever. Everybody took exactly the same courses up to the Abitur, the final examination. I cannot remember a single kind of elective. At another school a physics teacher had befriended me, if that's the right word, and I helped him prepare experiments. (One day, he disappeared without a trace. To this day I don’t know what happened to him.) But there were no electives whatsoever. That came after the war.

#### Being drafted into German armed forces, assigned to radar operation

Nebeker:
When did you get your Abitur?

Schroeder:
In 1944. Now came a very important juncture in my life. On February 2, 1943, German forces in Stalingrad capitulated. This battle cost some 300,000 German troops, of which only 100,000 were still alive. They went into Russian captivity, all but a few thousand coming back many years later. The Nazis said, "This is really no problem; we can easily generate another 300,000." How did they generate them? The battle of Stalingrad was drawn out, lasting two and a half months. During this time they made plans, and their main plan was to draft boys aged 15 and 16. The boys were to man anti aircraft guns and fire control radars, allowing the soldiers who had been doing this to go to the front. I was 16 at the time, so that's what happened to me.

On February 18, 1943, Goebbels gave his famous speech urging total war. Everybody cried, "Yes, yes, we want total war." On that same day, or maybe a day or two earlier, I was drafted and placed in an anti aircraft unit guarding a hydrogenation plant near Stettin, now Poland, on the Baltic. This plant was a huge enterprise, producing 25 percent of the German gasoline that was made from coal. The Silesian coal came down the Oder River and was converted to gasoline there. The plant near Stettin was surrounded by 18 anti aircraft batteries, each battery having up to 18 guns. Our battery had only six guns, the famous 88 millimeter gun. When I unpacked my bags, the battery commander—an Austrian captain—saw me unpack a book called Funkmesstechnik, that is, electrical measuring techniques. But Funkmess is also the German word for radar, so he thought I knew much about radar and assigned me to the radar. I did, of course, know something about electronics already, having built the transmitter and so forth.

My first war experience happened at this radar. It was in April 1943. I never liked to get up in the middle of the night, when the Allied planes came. Only when the final alarm sounded would I jump into my trousers with my pajamas still on and put a greatcoat around me. The guns were opening up from all of the other batteries around us, and there was a zing zing zing from their shrapnel. This shrapnel is very dangerous. They said, "If it hits your head, it comes out at your toe." These fragments were like razor blades. So someone put a steel helmet on me.

And then something very interesting happened, this first night when shots were fired in anger. I was at this radar, in charge of surveillance and target acquisition. As long as we hadn't seen any planes, I had to go around with the radar. Suddenly I saw planes on my radar screen. I was the first to see them, which was odd for a 16 year old boy while all the adults were in the dark. (There were no parallel monitors and my scope screen had a viewing hood that made it visible only to me.) Then I had to pick the targets. When they came within 10 kilometers the guns opened up.

Nebeker:
How did the guns get the information from radar?

Schroeder:
We were six boys at this radar. I was in charge of 'target acquisition'. That was my job. Once the target was acquired, I had to measure the azimuth. The guy next to me, a soft-spoken, dark haired boy, would measure the elevation, and a third guy would measure the distance (from the round trip delay of the radar pulse). There were two or three more guys; I don't remember what they were doing. In any case, information was transmitted by servos. We adjusted the radar and then servos would send electrical signals to what was called the Kommandogerät, which was really an analog computer. It had input either from optical or radar sources. In this case, the input was all radar because the hydrogenation plant had a great many tethered balloons (barrage balloons) around it and was covered by artificial fog, an acid substance that would get into your eyes.

Nebeker:
This analog computer took the information of azimuth, elevation, and range, and calculated where the gun should fire and what the fuse delay should be?

Schroeder:
Yes. The guns were operated at that point by Germans, but the guys who carried the shells were Russian prisoners. Somewhat earlier the Russians even pointed our guns. They were not forced to do this, but probably got better food if they volunteered. So we had quite a few Russians there, and we talked to them. I was amazed that some of them defended communism. I always thought communism was a bad thing, and here were these regular guys, who were fighting on our side, defending communism. Quite a shock!

Nebeker:
Had they learned some German or had you learned some Russian?

Schroeder:
They spoke German. I was amazed that some, not all of them, said that communism was a great thing, which I found ridiculous. At some point it was discovered that the Russians were not pointing the guns too well. So ever since they were allowed only to carry shells.

Nebeker:
The guns, then, were not directed automatically, but the information came from the analog computer to the gunners?

Schroeder:
At each gun there were two pointers, controlled by the computer, and the gunners had to move the gun so as to cover the pointers. Then the shell itself was put into some timing device, where the delay—controlled through the tip of the shell—was fixed. Then the shell was fired.

We fired 600 rounds that night, and presumably the other 17 batteries fired similar numbers of rounds. Not a single plane came down. Can you imagine that! The planes in the attack, actually not on this hydrogenation plant but on Stettin, the nearby major city. Something fiery did come down in the middle of the night, but nothing was found the next day, so we presumed that we may have hit an extra gasoline tank that was then jettisoned because it had caught fire. Since it was a night attack it must have been British planes.

The most interesting thing about this was the following. We had been trained on single targets. I remember once my father was visiting. There was a slow plane, a Junkers W 34, dragging an air bag, and we were firing at this air bag. Bearing and elevation were determined optically, and the distance was determined by radar. That was always more accurate. With the very first round that air bag came down. I don't know whether we hit the air bag or the cable. In any case, everybody was greatly cheered. We were immediately let off for the rest of the day. Yet in that night attack it was quite obvious that not a single plane—and there were hundreds—was brought down. My radar screen was filled with “blips” (reflections from targets). So I picked the biggest blip below 10 kilometers, and I told my elevation buddy next to me, "Let's take the target at 9.2 kilometers." But, we had to zero in slowly, because if we made a sudden change the analog computer would go wild. So we made a slow transition. By the time we arrived on that “target” it was gone. There was no peak at 9.2 kilometers. So I said, "Let's take the one at 8.7 kilometers." Again, a slow transition. Then that peak disappeared too. But suddenly a big peak at 9.8 kilometers. So slow transition, and then it too disappeared.

This continued the whole night. I had enough grasp of the situation to figure out that those peaks were not planes but the result of random wave interference. The words that I'm using now are based on my present knowledge, but it was quite clear to me even then that these peaks were the result of random interference from dozens or hundreds of planes accidentally building up to a big peak. Now if the planes changed a little in relative position, the phase delays changed, giving a different peak. I must have realized that, and the whole night we were shooting into thin air at these phantom peaks. But I was enough of a soldier, or whatever you want to call it, not to call attention to it. I was completely unpatriotic you might say. At the end of the night the battery commander, this Austrian, jumps up the earthen wall surrounding the radar, puts his arms into his sides, and says, "Boys, I've never seen such smooth data. This was wonderful!" He never mentioned that we hadn't shot down a single plane. We knew why it was smooth data, because we knew how to drive the servos, how a plane might fly, you know. So that's why the data was smooth and so the analog computer could do a good job at predicting where the planes would be.

Even as a teenager, I guessed what was going on, which required some technical insight. But I knew enough not to get mixed up in such a difficult and perhaps insoluble problem. How do you shoot at a squadron of 30 or 100 or more planes? This was a difficult problem, but I felt it was not my problem. I received a commendation for having delivered very smooth data. I knew the data were wrong and misleading in the true sense of the word, but it was not my problem.

Nebeker:
You were not wholeheartedly behind the German war effort at the time?

Schroeder:
I wouldn't go that far, but I would say that I certainly was not enthusiastic enough to jump up and say, "Look, we have this problem and we have to solve it, and I think such and such is going on." No, I didn't say a word. I thought, “That's for them to figure out.” You never knew in a country with a government like that. Maybe they would think it's sabotage or something. Even as a 16 year old I must have been smart enough to tell myself, "Stay away from trouble with these people."

Nebeker:
In this period from early '43 when you were drafted until the end of the war, you were not going to school?

Schroeder:
We had school at the same time, so it was a tough life. In the morning we had school—though a reduced schedule—and in the afternoon we had radar and other training. Then at night—not every night, but many nights—the planes were coming and we had to get up. But as I said, I didn't always get up.

Nebeker:
How many times were there over flights and how many actual attacks?

Schroeder:
While I was there, which was only from February 16th or so to October 22nd (1943), some eight months, I witnessed or participated in only one attack, the one that I just described on April 22, 1943.

Incidentally, there was an interesting incident that shows how naive we were. The next day was our day off. We always went to Stettin to have a bath and go to the local cafe, where the band played highly forbidden tunes like Tiger Rag and the Black Panther. It was publicly known that the Nazis permitted a few infractions like that, which made life a bit more bearable. So the next day we wanted to go Stettin. "The buses aren't running," the sergeant told us. "Why?" Because, he said, "The buses are transporting dead people." We said, "Dead people?" He said, "You remember the attack last night? You know Stettin? Thousands of dead people." In other words the whole night we were shooting, but did not realize that this meant that some city was being attacked. We went back a week later, and I saw my first houses destroyed by bombs.

Nebeker:
What happened after October of '43?

#### Volunteering for aviation and radar training

Schroeder:
Well, in July I volunteered for a flying course, since my father had been a pilot in World War I. I wanted to become a pilot, a fighter pilot if possible. I was accepted into a glider school, and so I flew gliders. It was marvelous. In the middle of the war—blissfully ignorant of the general suffering—I'm sitting there in my glider high above Pomerania trying to locate the church spires. They were not on the horizon where they had been before I took off. They were below me, and I got lost.

Then in August or thereabouts came a letter to all German youths of my age asking whether we had any experience in electronics and whether we wanted to volunteer for a special radar school. Well, I had that background, so I volunteered. I ended up in a special school in the Westerwald near Cologne, half a day for regular school, half a day for electromagnetic. For six months we were intensely trained in Maxwell's equations and all that. At the next school, we studied all German radars and Allied radars as far as were known. Even to this day when I meet an American radar expert I can sometimes talk with him about various circuit details.

In May 1943 the Germans had shot down an airplane with PPI (plan position indicator) radar, an American radar that provided a survey picture of the ground. It had not been destroyed, so the Germans rebuilt it and installed it on top of a flak (anti aircraft gun) tower in the Zoological Garden in Berlin. From there it could produce a map of Berlin. Goering was shown this and was flabbergasted, thinking, "No wonder they can bomb the German cities even in fog and at night." At that point—the summer of 1943—he was in charge of German war research. As president of the Reich Research Council he had sent the letter to which I responded.

So we took this special radar training. We were then supposed to close the gap between British and American radar technology and the German technology. At the beginning of the war German and British radar were about equal. But Goering said, "We don't need those boxes with coils inside"—that's how he referred to radar—and he stopped the German radar development. "What we need are brave men," he said, "And those boxes with coils inside we don't need." Then in '43 he discovered that those boxes could show a map of Berlin, and he tried to undo his earlier action.

Nebeker:
What was the name of the school?

Schroeder:
It was called Lehrgang, the German word for 'training course,' and the name of it was Prince Eugene. That was just a code name from the famous Austrian general and French born prince who beat the Turks some 300 years ago.

Nebeker:
Was it connected with a major R&D center?

Schroeder:
No, there was no R&D going on. There was just teaching. Of course, we were all smart boys, and sometimes we would invent some little thing. We never saw Goering, but we saw the people directly below Goering who came and visited. This, as I said, was Goering's baby.

I remember a visit from one of the higher ups. The guy in charge under Goering was a General Martini. He visited the school. When he saw how pale we were—besides school and radar training, it was a kind of military boot camp—he said, "You boys have to go to the Alps and ski." So we were all sent off to the Alps for three weeks.

Because school continued, I was able to get my Abitur, the final school leaving examination on April 30th, 1944. This was unusual. The program was shortened somewhat, but it was a regular Abitur, which required the presence of a school director, the district chief, and so forth.

Nebeker:
Were you able to start university schooling then?

Schroeder:
No. We were sent home for the first two weeks in May for vacation, and then we were supposed to report back for Air Force boot camp, six weeks or so, and then Luftnachrichtenschule, Air Force Communication School, Detmold. In other words, more training. But during those two weeks at home I contracted rheumatic fever and had to stay in the hospital for six weeks. That was when this June 6th episode occurred, the radio on my nightstand.

Nebeker:
I see.

Schroeder:
After the hospital stay there was six weeks of convalescence. In the meantime I was afraid of losing contact with this special radar group. The prospect of being drafted to some other unit and being sent to the eastern front as cannon fodder was more and more frightening. Things actually got even worse than that. It must have been the last days of July '44 or maybe the first days of August. I was called up by the Waffen SS (the military branch of the SS). It is not widely known, but towards the end of the war the Waffen SS would not only take volunteers—highly motivated Nazis, let me say—but also draft young people. I don't have any figures, but my best guess is that towards the end of the war roughly half the Waffen SS, if not more, were draftees.

That, of course, was the last thing I wanted. So my convalescence was cut off from one day to the next. My parents took me to the train station to meet the night train coming from Krakow, Poland, going to Berlin (where I changed trains to Detmold). The train was so full they had to push me in. My mother said, "We are crazy! We are pushing our son into the war, into his grave." But the truth was different. After I was on that train, my father went home and answered the draft call from the Waffen SS saying, "You are too late. My son has already left for his Air Force unit." This saved me, because I would otherwise have ended up as cannon fodder.

Nebeker:
You rejoined that radar unit?

Schroeder:
Yes, at the Lufnachrichtenschule Detmold. Now just before I left, we had gone swimming and I had stepped on a glass shard, which cut my toe. There was still boot camp there, and this toe got more and more infected. I didn't say anything, because I was afraid they would send me away from that unit. But the thing finally got so infected that I couldn't walk anymore. I was driven to a hospital, the villa of the Prince of Lippe Biesterfeld, who had married the Dutch queen Juliana.

The toe was operated upon, and after a week or two I went back to my unit. In the meantime the unit had concluded boot camp. Here I was with just four or five days of basic training. What should they do with me? The German Air Force had an agreement with the Navy that 10 percent, or whatever percentage it was, of these boys would be turned over to the Navy for their radar services. What the Air Force got from the Navy in return was their agreement not to draft such people. Now there were many volunteers who preferred going to the Navy rather than the Air Force. But in my case, the Air Force didn't want to see me anymore, and they turned me over to the Navy against my will. Of course I wrote home that the authorities wanted to send me to the Navy. My father, an old pilot from World War I and a former Air Force officer, was incensed. He said he would write to the Luftwaffe personnel office in Berlin and have the order rescinded.

By now I was 18. I did a very smart thing. I wrote to my father, "Look, these are such uncertain times. Why make a big effort with the Air Force personnel office? Who knows? Maybe I am better off with the Navy. It's all unpredictable anyhow." So my father didn't write and I stayed with the Navy. As it turned out this saved my life, because my buddies who stayed in the Luftwaffe, a great many of them fell. They were at the Luftnachrichtenschule Halle in April of '45 when the Russians and the Americans converged from both sides. These were not really soldiers, but technical people. They were mowed down. They were sent against the Americans, and many of them lost their lives on April 11th and 12th. Taken from the school benches and sent against the Americans, who by then were fully experienced fighters. I visited their graves a couple of years ago when East Germany became more accessible. But I went with the Navy, and it was a much better service then.

Nebeker:
Where were you sent?

Schroeder:
I was sent to Stralsund. There, too, basic training was just concluding. An admiral came for the final inspection, and there were two or three others like me who had missed boot camp or most of it. We were at the left side of this formation, and the admiral was told something like "Don't look too closely at those guys; they missed the whole thing." So then for the warlike demonstration, I was used as a target. Even though this was the Navy, we had to throw hand grenades, and they needed targets. There were these foxholes, and I was put into one of them. Others were to throw hand grenades at me. One of the grenades hit the earth wall behind me and rolled down into my foxhole. I was crouched down there. The grenade was sizzling under me.

Nebeker:
It had a fuse, but no explosive charge?

Schroeder:
It did explode, a flash and then a cloud so that you could see what you had hit—at night the flash and in daytime the smoke. That thing was sizzling there, and, I mean, I knew enough biology. So I jumped out of the foxhole and the thing went off. Of course it didn't hurt me. Everybody was laughing his head off, including the inspecting admiral. He said, "This is exactly what the enemy wants you to do. You would have been mowed down by now." I didn't say anything. I knew there was nobody there to mow me down. I didn't mind being the butt of their jokes. I was still in one piece, and, one might add, a potential father.

One of the few radar inventions made by the Germans during the war was what we called the dielectric antennas. They look like fingers made out of acryl, a little dipole at the end, usually four of them, which rotated under a kind of a cheese bell. Four dielectric fingers rotating under a cheese bell—this is what the German submarines had. Now in a storm these fingers would sometimes break off. According to radar regulations, every German submarine had to stock so and so many condoms, which would be placed over these fingers if they cracked. (This regulation, however, turned out to be redundant.)

Another revelation from those days was the saga of the Metoxradar receiver that a French firm had built for the Germans. The German submarines, as I said, used no active radar, but very sensitive, highly directive rotating radar receivers. But in the Metox receiver there was a little wire, which connected the local oscillator in this highly sensitive, super heterodyne receiver to the transmitting antenna. The Allies knew the oscillator frequency, so they could detect this Metox receiver, even though it was supposedly a passive set.

Nebeker:
Did the Germans discover this?

Schroeder:
Yes, so the receiver was no longer used after too many submarines were lost. I don't know what happened to the French resistance people who did that. The story of the Metox receiver was something we learned at that radar school.

Nebeker:
When was it you were at that school?

#### Radar station deployment

Schroeder:
It was early August '44 that I was pushed onto that train. Around September 30th, I was turned over to the Navy; and on January 12th, 1945 the radar school was finished. At that point we were split up by the alphabet. My friend von Behr ended up on a submarine tender near Danzig. I was sent to Holland, to a coastal radar station near Hoek van Holland. These were huge installations made by German bridge construction companies. I forget how high, maybe 40 meters, or 120 feet, high. The antennas were for fairly long wavelengths, around one meter, which is why the antennas were so large. The antennas were steerable. They had what we called Posaune ('trombone' in English) to change the delay and thus steer the radar beam.

Nebeker:
This was electrical, rather than mechanical, steering?

Schroeder:
Yes. These antennas were huge steel constructions on cement bases, so all steering was electrical. We could pick up planes over Britain as soon as they were a few hundred feet in the air. This was general surveillance, not fire control, radar.

Nebeker:
I see.

Schroeder:
We had particularly powerful radar called Gigant (“Giant”), and then we had Würzburg Riese, that's Würzburg Giant. Then there was the Rotterdam Gerät, which was a copy of that captured American PPI radar but with German tubes. The American 6AC7 tube was replaced by the German EF14, which has similar characteristics, variable mu, high gain.

Nebeker:
There happened to be a comparable German tube?

Schroeder:
Yes. The German EF14 replaced the American 6AC7. In April '45 the duty assignments were supposed to be switched. In other words, my friend was supposed to join coastal radar, and I was supposed to go to a submarine base in Denmark. So we reported to our commander for these radar units, a Navy Kapitän zur See, a rank comparable to Army colonel, a nice family man. He said, "You want to go from Holland to Denmark? Haven't you heard who controls the airspace?" and so on. “We have just had two speedboats between Holland and Germany shot to pieces.” He said, "You boys stay here. Disregard that order." So we stayed in Holland, and I don't think we would have made it had we tried to transfer. This was four weeks before the end of the war.

We stayed there and capitulated on May 5th to the Canadians. On June 6th I was supposed to be sent back to Germany, but I didn't want to go back. I did not know where my parents were, whether they had escaped from Silesia. We had a house in West Germany, but I didn't know if it was still standing. We had heard about the prisoner of war camps in Germany where people were starving and where there were epidemics. In Holland, on the other hand, we were on Canadian army rations.

So I didn't want to go back, and fortunately the Allies wanted six radar experts from our unit for the job of turning the station over to the Allies. They had picked people who didn't know the first thing about electronics; one of them was a butcher by trade. A friend of mine stepped forward and said, "There are three of us here who know everything about radar. Those guys don't know the first thing about it, and they want to go home to their wives and children." So on the spot the Allies decided, "Okay, you six guys board the ship for Germany, and you three guys stay back." So I spent the next two years actually, longer than I wanted, turning over radars to the Allies.

We were not prisoners of war, but “capitulated military personnel,” which meant that we got vacation among other things. So in October 1945 I went to Germany, by ship to Hamburg and then by train. I found that the whole family was alive and the house was standing. I cried with joy. I told them I'd be back for Christmas. But in the meantime so many people who had been sent on vacation hadn't returned—especially the ones who had relatives in East Germany, because Soviet military police wouldn't cooperate and capture them—that I had to stay for another year and a half until April 15th, 1947.

Nebeker:
Where were you in Holland?

Schroeder:
Ijmuiden, not too far from Amsterdam.

Nebeker:
Your job there was to assist in turning the stations over to the Allies?

Schroeder:

So we built up one of these Würzburg Riese radars and tested it on targets. Everything was fine; it was working perfectly. Then our immediate superior, who was just a sergeant, alerted all of his superiors. I guess he had to get permission for this work from his higher ups anyhow. Now that the thing was working, we were visited by 13 higher Dutch Navy officers—we counted the stripes, a total of 31 or 32 stripes. Of course the Dutch who were fighting on the Allied side in England knew all about radar, but not the Dutch who had stayed behind.

When we demonstrated the radar, there happened to be some fishing boats off the coast. We measured the distance of the boats; it was 7 kilometers. There was one older Dutch captain who said, "No! I have been on the sea for 40 years and I can tell that the distance is at most 3 kilometers." We said that we calibrated the radar and that the distance was indeed 7 kilometers. "No, it's 3 kilometers," he came back. Suddenly there was almost a fight. We knew the radar was working, and he had 40 years experience at sea. Then one of the other Dutch officers spoke to him in Dutch—by this time I understood Dutch pretty well—that he should take into account that he was not at sea level but at a considerable elevation, so the perspective is different. "What looks like 3 kilometers might in fact be 7," he said. This saved us, because then the old captain gave in.

Everything worked fine, and we offered the Dutch to keep it operating for the purpose of guiding traffic into Ijmuiden harbor in fog and at night. They were very much impressed and said this would be wonderful, but they were bound by higher orders. Everything has to be dismantled. This order came from the British. In the summer of 1945 there was considerable fear that the Soviet army would roll right on, occupying the rest of Western Europe. Then all the German guns and radars would be in Soviet hands. So the British insisted that all radar stations, including our beautiful radar, be razed. That's the end of the radar story.

Nebeker:
It's interesting that so many engineers, or future engineers, ended up working on radar during the war.

Schroeder:
For me it all started with observing my friend listening to the whole world on his short wave radio and wanting to do the same thing.

Nebeker:
When were you finally released by the Canadian or Dutch authorities?

Schroeder:
We were of course getting impatient. It was now 1947, and it was a very severe winter, and the Elbe River was frozen over. At that point the Dutch wanted to or had to—perhaps by some agreement—set us loose. In any case, I remember a speech by a higher Dutch officer to the remaining German radar and other experts. He spoke in Dutch—which we all understood by that time—the famous words, "As soon as the Elbe is free of ice you go home." Finally, on April 15th, 1947 that happened.

Of course I went home to my parents. A few weeks later I went to a German discharge camp in Münster in the Lüneburg Heath. As the spoils of World War II—I'll never forget—I got one pair of woolen long johns, a pair of socks, and one blanket.

Nebeker:
That's what you got on discharge?

Schroeder:
Yes, and—not being the farming type—I much preferred the long johns over a farm in Kazakhstan that everybody had been promised by the Nazis. And the blanket came in very handy. We dyed it dark blue, and it became a beautiful coat for my sister.

Nebeker:
Those were hard times?

Schroeder:
Yes, this was two years after the war and I had missed the worst times, but there was still not enough food. My mother was a good provider, so we never actually starved. I remember traveling around with my father. He had friends in the Westphalian zinc and enamel industry, where they made kettles and pots and enamel ware. These were old tennis buddies of his. They gave him all these pots and pans. We would board a train with them and sell them to farmers, or rather trade them for a ham, eggs, honey—you name it. So we survived. Other people sold their rugs. There was a joke that the farmer said, "No, I don't need any more rugs; I don't have enough cows to stand on them." Good rugs, Persian rugs.

### University education

Nebeker:
Did you manage to get to a university then?

Schroeder:
Yes. That was the next thing. It was not the nearest university, but one not too far away: Göttingen. It was a university I was much attracted to. My best friend was there, and its faculty included five Nobel Prize winners in physics and chemistry—people who had been interned in Britain but then shipped back to Germany in 1946. They had congregated in Göttingen: Werner Heisenberg, Max von Laue, Otto Hahn, Adolf Windaus, and Max Planck (who was not interned). And of course Göttingen was a famous university, even before Gauss, Riemann, Minkowski and Hilbert added mathematical luster. I went to Göttingen with my father.

By now I was almost 21, but still my father had to come along. After four years in the war, I was back in the lap of the family. To gain admission to the university, you first had to pass an examination—they wanted to see how good you were. I had an appointment with a Professor Becker, who had written a book on electrodynamics. Before entering his office, I was intercepted by his assistant, one Dr. Leibfried. He asked me, "What did you do during the war?" Now, he didn't want to hear about military service, but how I occupied myself scientifically during the war. I said I worked with trigonometric series. He said, "What did you do?" I told him how I worked out addition theorems for sine and cosine series and other trig functions, things like sin x plus sin 2x plus sin 3x and so on. This is an important formula for antenna arrays, which is how I must have become interested. He said, "You never heard of the complex exponential function? If you write the series for a complex exponential, then you can apply the formula for a geometric series, take the imaginary part, and get the sine series result." I said, "That's right; I didn't think of it." At that point I thought that I had blown my chance; that I would never be accepted, especially since I could see my mistake. "How stupid can you be?" I thought.

At that point Professor Becker appeared. "Hi there Schroeder, please come into my office," and "What did you do during the war?" Exactly the same question. This time I stayed away from trigonometric series. I said I was interested in LC circuits and so forth. I don't remember whether I mentioned the transmitter. I explained: here's the magnetic energy and the electric energy, there's radiation and damping and so forth. I talked for about 15 minutes, and then he said, "Okay, that's enough." At that point I was so shy and fearful that I thought that his "that's enough" meant that I had proved that I didn't know very much. That's how I interpreted it, but still I wanted to know my chances. My future life depended on being allowed to study, and at that time there were many more people—soldiers coming back from the war—applying to universities, than could be accepted. So I said, "Herr Professor, what is my chance to be accepted?" He then said something that of course I will never forget: "If you are not accepted, nobody will be accepted."

Nebeker:
That was quite an honor. Did you study physics?

Schroeder:
Yes, and here comes an interesting story. I was always a crypto mathematician. Even though I was studying physics, I was always taking extra math courses on the side. Already during the third semester I was ready to take my Vordiplom, a kind of a B.S., for which, however, you needed chemistry. One usually did this after six semesters. I went to Professor Becker and said, "Professor Becker, I could take my Vordiplom already now except for chemistry." I told him that I hadn't attended the chemical laboratory course. I didn't go because it stank, it was unheated, and I hated chemistry. He said, "Okay, you can proceed without the laboratory course as long as you know enough chemistry." Then I said, "But I never went to a single lecture in chemistry." He said, "We've never had a case like this before." Then I said, "But I have attended a number of extra courses in mathematics, like complex function theory and probability theory," which was way beyond third semester. "Well," he said, "then why don't you take your Vordiplom in mathematics?" I said, "But I want to become a physicist." "That's very simple," he said. "On the day of the examination you are a mathematician, the next day you are a physicist again." Today that would be impossible. Everything is more bureaucratic.

Nebeker:
I see.

Schroeder:
So I have my B.S., if I thus translate Vordiplom, in mathematics, but the rest was physics. But for my Ph.D. chemistry raised its head again. At that point I was 27 and not inclined to start chemistry, which I had hated all my life. So I went to my professor, Erwin Meyer, and said, "Look, I am not going to start chemistry now."

Nebeker:
Your professor was Erwin Meyer?

Schroeder:
Yes, he was the director of the institute and as such my own predecessor there. He was on my side. After a little thinking he said, "At the end of a very long faculty meeting, I will bring this up." In the meantime I had an offer from Bell Laboratories. "I will mention that you are emigrating to the United States, so in other words we won't see you again." A week later, the day after the faculty meeting, I went to him and asked, "How did it go?" He had told me before, "I have to be careful and can't guarantee it because we have these wandelnde Gewissen, walking consciences, in the faculty." The nitpickers and so forth. He said, "It went just as I hoped. It was a very long meeting; everyone was anxious to get home. At the very end I brought this up and everybody okayed it."

Then Meyer said, "But, you know, you really should know some chemistry." I was in a conciliatory mood and said, "Yes, professor, you are right. I should know chemistry." At that point it didn't cost me anything to agree. In retrospect I would call my attitude outright silly, especially considering the deep mathematics in chemistry (just think of group theory) and the beauty of the subject itself. Later, when I became his successor, one third of my students were working in membrane biophysics and things of that nature that contain a heavy dose of chemistry. That is to say, suddenly I was a supervising student working in chemistry. So I had to read up very quickly to fill that gap. Ironically, a year later I was elected a Scientific Member at Large (Auswärtiges wissenschaftliches Mitglied) of the Max Planck Institute for Biophysical Chemistry. But I never did take a course that I didn't like; if you like something, it's much easier to learn. (The concept of “credit” courses is unknown at German universities.)

### Bell Labs employment

#### Job offer

Nebeker:
How did you come to be offered a job at Bell Labs?

Schroeder:
Well, before being accepted into an institute to do your Master’s thesis, at that time—it's no longer the case—you had to build up some new laboratory experiment. In those years there was no institute at Göttingen with equipment for experimenting with microwaves. I was supposed to build the first laboratory experiment involving microwaves in hollow metal tubes. We had some magnetrons and klystrons and round waveguides. I said to Professor Meyer, "Round wave guides, that means Bessel functions." If there's one thing I don't like—I always had strong dislikes—it's Bessel functions. Meyer replied, "The only thing you have to know about Bessel functions is 1.84 and 2.40. One is the first zero of J0 and the other is the first maximum of J1." This was basically true. You didn't have to know much about Bessel functions.

I built up this experiment and discovered that in the so called H10 mode—it's now called TE something—the basic mode in a waveguide, with a plunger at each end, I always got two resonances. Nobody could tell me, not even those in theoretical physics, why I always got two resonances. I finally had to explain it myself: the basic H10 mode has an electric field existing in two polarizations, and if the wave guide is not perfectly round, then there will be two modes separated by a few dozen kilohertz. The radiation was at 3 centimeters, in other words, 10 gigahertz. But the tubes were not perfect, so that's why I always got two resonances. That was my explanation. The situation is similar for the circular membrane of a microphone or a drum, where the basic mode is degenerate.

Now if that was true, I reasoned, then I should be able to put a little wire loop and a diode in one of my plungers, so that if I turned it I could pick up one mode or the other. It did not work as expected, though. My theory was shot through. But it had to be true, I thought. It then occurred to me that maybe the major deviation from perfect circular symmetry was my asymmetric wire loop, my little wire loop picking up the magnetic field. So I changed the geometry. I left the resonator untouched and took the magnetron, quite a heavy thing, and turned it. Everything then worked just as predicted. When I demonstrated this to Meyer, he said, "This is marvelous. You should go to America. That's the microwave country." The thought had never crossed my mind, but that comment put a bug in me.

A short while later I heard that a commission for the Fulbright Fellowship was in Göttingen interviewing students. Of course I applied. There was a Fulbright representative and the head of the English Department at Göttingen, a German. They asked me all kinds of questions. My English was pretty good, no problem with that. My academic records were first rate. But there was something else they wanted. They were looking for politically involved students who would spend a year in the United States and then come back and tell everybody what a wonderful country the U.S. was, that kind of thing. I was asked how many political rallies had I attended. I had to think a while. Then I remembered I had gone to a rally when some students of theology, Communists, came back from a party congress in East Germany. Many students went to that rally to debate the Communists. The Fulbright commission pricked up their ears. Yes, I was politically interested, and it was an anti Communist action. Then the American interviewer asked me, "Afterwards what did you do?" I said, "I went home." I think they wanted to hear that afterwards I participated in further discussions. But I wasn't that much interested in politics. I was working at home “pulling little roots”, as my mother used to say. I never heard from them again. I don't think I even got a letter of rejection.

In the meantime I heard about Bell Labs, with people like Bill Shockley, S. O. Rice, and Claude Shannon. Those were the three names I knew. I asked Meyer whether he couldn't recommend me to Bell Labs. He said he had had a student in 1938 who wanted to join Bell Labs; Meyer was then a professor in Berlin. So at that time he had written to Bell Labs, and Bell Labs had written back saying they didn't hire foreigners. Well, he took it at face value, and I took it at face value. In retrospect I think that perhaps this student wasn't good enough. It is also possible that the student may have been Jewish (1938!), and his rejection may have had something to do with that. (Did you know that Richard Feynman had not been able to get even summer work at Bell Labs the first time he tried?)

Nebeker:
Right.

Schroeder:
That seemed to be the end of my attempt to work at Bell Labs. Then a year or so later, I heard that Bill Shockley was in Göttingen looking for bright physics students. Actually Shockley and Jim Fisk, later president of Bell Labs, traveled to Europe in the spring of 1954. Fisk went to Heidelberg, where he had studied, and Shockley went to Göttingen. Maybe they went to other places, too. When I heard about this, I ran to Meyer, who said, "I will have to write to the director of acoustics research at Bell Labs—someone called Winston E. Kock—and I'll put in a few lines for you." I was on very good terms with Meyer's secretary; later she became my secretary. So I asked her, "Did he remember putting in a few lines for me?" She said, "He put in a whole page for you."

About two weeks later I got an invitation to meet Win Kock in London, in the lobby of the Dorchester Hotel. He asked me about my thesis and so forth. I asked him about the Bell System. He said, "Well, there is AT&T and there is Western Electric and there are 23 operating companies, like New Jersey Bell and Southern Bell and..." During his recitation he stopped in the middle of the sentence—we were sitting in the lobby of the Dorchester. He was looking at something very intently, turning his head slowly. It took about two minutes. A young lady had appeared at the far end of the lobby, crossed the whole lobby, and then disappeared through the revolving door. He stopped in mid sentence, stared for a minute or two, and then suddenly resumed, "... and there is Southwestern Bell," and so forth. I found this remarkable, and I must say that the opinion I then formed of my future boss, I never had to revise it.

Exactly 25 years later I went back to the lobby of the Dorchester Hotel. April 25, 1954 was the original day, and the lobby was still there. At the end of the lobby there was a kind of a hatcheck counter. An old lady was behind it. I went up to her and said, "Could it be that on this day, April 25th, 1954, a Sunday, 25 years ago, a young woman might have appeared from the door behind you—it was about 2:00 p.m.—and crossed the lobby and then exited by the revolving door?" She must have thought I was from Scotland Yard or something. She said, "Oh yes, of course: 2:00 p.m. was the change of shifts then." This entrance was for the service personnel, chambermaids and so forth. I asked her, "How do you know this?" She said, "I have been here for 30 years."

Anyway, Kock had to go to Scotland on military business, underwater sound business—maybe at Loch Ness—and he told me that since I was a foreigner, the Bell Labs president—Mervin Kelly at that point—would have to approve any offer of employment, which would take six weeks. To the day, six weeks later, in early June 1954, I got a letter from Bell Labs offering me a job at \$640 per month. I could have gone to Siemens for 500 marks a month, but here was a better company offering me five times as much, so of course I accepted. I would have gone for nothing.

#### Reception of Master's and Ph.D. research

Schroeder:

Now comes the next surprise. In the meantime the Acoustical Society of America had its 25th anniversary, and my boss, Erwin Meyer, was invited to give a kind of a keynote speech on acoustics research in Germany. In this speech he mentioned a number of things that I had done in my Ph.D. thesis and subsequent research.

The result was that I became known in the States. I was almost a bit famous. So when I arrived at New York harbor on the Andrea Doria—still afloat at that point—there was my director Win Kock and my supervisor Ralph LaRue Miller and a long black limousine with a uniformed chauffeur. I was probably one of the few immigrants received in such style. Then we went to the Newarker Restaurant at Newark Airport, one of the best restaurants in the '50s in this whole area. I had never been in such a restaurant, and I couldn't read the menu, most of it in French. I did, however, recognize one item in German called bratwurst, so I had bratwurst. Kock was a very polite man, so he had bratwurst too, and we all had Löwenbräu beer. So, even with the sparkling deserts at the next table, I felt kind of at home, while the limousine was waiting outside. After lunch I was put on the payroll and I had to borrow \$20 from the head of technical employment, Homer Smith, because I had arrived in the U.S.A. with just \$2.30 in my pocket. That was my first day at Bell Labs.

Now my Master’s thesis was built on the observation, mentioned earlier, that in a round waveguide there are always two degenerate modes very close together. I had some mechanical trimming device so that I could put them on top of each other within perhaps 10 kilohertz. That's a very high accuracy; when the radiation is at 10 gigahertz, that's an accuracy of one in a million. Then I would put some dielectric material into the waveguide. The two modes would split up, and I could measure the frequency split and thereby determine the dielectric constant with very high accuracy. That became my Master’s thesis. As you can see, it was homegrown.

But I had always had an interest in statistics. I got hold of an old U.S. Army biscuit tin, about two feet high, a huge thing. I put my 3 centimeter microwave antenna into this tin, which was closed except for a little hole, and I saw thousands and thousands of resonances. I became interested in the statistics of these resonances: how are they distributed in amplitude and frequency and so forth. The average number, of course, is given by a famous mathematical formula due to Hermann Weyl. So the average distance is fixed. But what is the distribution, or at least the second moment of the distance distribution between adjacent resonances in a large box like that. This formula of Weyl, which is really for undamped systems without losses, is that valid for systems with losses?

Anyway, I went to see Franz Rellich, quite a well-known mathematician, and asked him about it. He took about 20 minutes to search the library and at the end said, "I'm sorry, there doesn't seem to be any theorem for the complex-eigenvalue (lossy) case. The Weyl formula is for real eigenvalues (the lossless case)." Well, that was too bad. Then he said something very interesting—this was in 1952, when I was beginning my Ph.D. thesis—he said, "Do you know that you are the first physicist since the early 1930s who has come to a mathematician asking a question?"

The point that he was making was this. Before 1933 there was intimate contact between the mathematicians and physicists: David Hilbert, Hermann Weyl, Emmy Noether, and Richard Courant on the mathematics side, and Max Born and Werner Heisenberg and so forth on the physics side. They had a joint seminar every week. They talked to each other. But after 1933 everything fell apart. Hilbert was invited by the Reich Minister for Education to Berlin and Rust, a well known Nazi, asked Hilbert at dinnertime, "How is Göttingen mathematics?" Hilbert gave a classical answer: "Herr Minister, there is no mathematics left in Göttingen." On the whole one might say that Germany became a comparatively dull country after the Jews had left, an effect that, I believe, persists to this day.

Nebeker:
Yes, Jews and others, including Weyl, had been driven out or had left by their own choice.

Schroeder:
Yes, and Hilbert could get away with such a remark. So in 1952 I was the first physicist—albeit young and unknown—to talk with a mathematician in a long time. My Ph.D. thesis topic became the statistics of the normal modes in irregular cavities. My boss, the acoustician Erwin Meyer, wanted me to do a thesis in acoustics. I told him I was not interested in acoustics. Acoustics and chemistry were on the same level for me. I thought, completely mistakenly, that there was not enough mathematics in it. I told Meyer, "I want to investigate the distribution of these modes in large microwave cavities." He replied, "Well, that's wonderful. We are interested in the distribution of normal modes in concert halls, but we can't measure them because the Q isn't high enough. The modes are not resolved in a concert hall."

In a concert hall in a 1 hertz frequency interval you may have a thousand modes, but of course the bandwidth being 1 hertz, you see only one peak. That is, you see a random interference, a thousand modes producing one peak. It's exactly the problem that I had discovered that night at the fire control radar. So Meyer said, "You do your microwave studies, but it's really some concert hall questions you are answering." That's why, when my thesis was published, it was called "The Distribution of Resonances in Large Enclosures," as main title, and "Model Experiments with Microwaves," as subtitle.

Nebeker:
The analysis was general, or at least common to those two situations?

Schroeder:
There is no difference really, except for a factor two, because in the electromagnetic cavity most modes come with two polarizations, while in the acoustic modes you have only one. The Weyl formula says basically that for every acoustic mode you have two electrical modes.

Nebeker:
Does it often happen that mathematical results can be thus transferred?

Schroeder:
Yes, in fact this was Meyer's main teaching philosophy. It was also Win Kock's philosophy as a director of acoustics research at Bell Labs. One of the microwave antennas for the transcontinental microwave link that he invented was based on acoustic concepts, and, conversely, he built some acoustic lenses based on microwave concepts. These guys, Win Kock at Bell Labs and Erwin Meyer at Göttingen, and others believed in the complete congruence of microwaves and acoustic waves. Occasionally a factor of two would pop up, but otherwise the phenomena were similar. Of course electromagnetic wave diffraction depends on how the E field is polarized. But on the whole it's rather similar.

Nebeker:
It seems safe to say there is cross-fertilization.

Schroeder:
Absolutely. My Ph.D. thesis dealt with microwaves, but the question I was answering was in concert hall acoustics. I discovered against my expectation that the spacings of adjacent resonances were not exponential (like the intervals of consecutive clicks in a Geiger counter next to a radioactive sample), but was a distribution that went back to zero for small spacings. This was already called then, though unbeknownst to me, the Wigner distribution. It's now a very well known concept in nonintegrable systems, in chaotic dynamics. This is very up to date. This kind of distribution was postulated in 1935 by Eugene Wigner in Princeton as the distribution of the energy levels in complex atomic nuclei. I rediscovered it as the resonance spacing distribution in microwave cavities or concert halls. Now it is recognized as generic, that any so called chaotic or nonintegrable dynamic system has that kind of distribution. But the twain didn’t come together for a long tome. (The same distribution also governs the zeroes of the Riemann zeta-function, something that Hilbert had postulated around 1900 and that was confirmed numerically by Andrew Odlyzko at Bell Laboratories.) This was some of my work that Meyer had mentioned in New York in 1954. Much later, I rekindled my interest in chaotic systems and, in 1991, wrote a popular book on the subject,Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise.

#### Bell Labs research

Nebeker:
What did Bell Labs want you to work on?

Schroeder:
Bell Labs wanted me to continue along the lines that I just mentioned. But at the time I thought—completely erroneously—that I had solved all the problems about the modes and so forth. I thought I should do something of fundamental interest to Bell Laboratories, and I elected on my very first day at Bell Labs to go into speech. I felt this should be of interest to the telephone system, and it was something new.

So I started speech research. After two years or so I discovered I couldn't really make my speech synthesizers sound better if I didn't know more about the human ear, so I got into hearing research. Then quite a few years later we were starting to think about speakerphones and conference telephone arrangements. Then room acoustics came in again. So the main parts of my career at Bell Labs dealt with speech, hearing, and room acoustics, in that temporal order. But I had many other interests, like computer graphics, which I pursued at the same time.

Nebeker:
Were you able to choose your own research topics?

Schroeder:
Yes. In those days in the research department the guys who knew or thought they knew what they were doing were left alone. I was supposed to join an effort by Win Kock on a future picture phone in 1955, which among ourselves we called "phony vision." It was called "phono vision," but we called it "phony vision." It was a single low resolution frame every 2 seconds going over the telephone line. An awful thing. I told Win Kock—although he was my director and I should have been grateful to him for bringing me to this country—I simply said, "No, I will not join that effort." I've always been willing to say no, whether it was chemistry or whatever. Furthermore, I said to Kock, "I've been here now almost a year; I was promised some technical help, and I haven't seen any technical help." So instead of joining his effort, I finally got my own technical help, an able technician called Tony Presti.

Then I built my first vocoder (from VOice CODER). I fell victim to the kind of self delusion that is described in Aleksandr Solzhenitsyn's book The First Circle. I thought the speech synthesizers that I was building were intelligible. Well, I knew what they said and I was used to them. In retrospect I believe that they were almost completely unintelligible to others. I still remember a visit from my new director, Axel Jensen and Mervin Kelly (president of Bell Labs). I was so proud of my synthesizer and demonstrated it to them. They were very polite, but I'm pretty sure that what my machine was saying was unintelligible to them. Later things got a lot better when Max Matthews joined us (in 1955) and introduced digital simulation, which circumvented the pitfalls of analog circuits. Using digital simulation, Ben Logan and I designed a speech compressor with a total of 400 narrow band pass filters that could speed up speaking rates by a factor two and that we made available to the American Foundation for the Blind for their Talking Book program. We also invented sophisticated artificial reverberators that simulated sound transmission in concert halls. Talk about signal processing! Thousands of times real time on the computer.

#### Speech synthesis

Nebeker:
Why was Bell Labs interested in speech synthesizers?

Schroeder:
First of all, we were interested in speech because that's what was being transmitted. Also, even in the '50s, we wanted to have voice dialing. The efforts to achieve automatic speech recognition were, at that time, failures. Now, 40 years later, there is some hope. For example, in a car it would be nice if you could dial by speaking the number. And today there are some services that involve automatic speech recognition. You speak a name, and the machine recognizes the name, that kind of thing. We were looking ahead. We were working on speech synthesis because by taking speech apart and synthesizing it again at the other end we could compress its bandwidth by a factor of 5 or more.

Nebeker:
I see.

Schroeder:
Consider the transatlantic cable. The first one had, let's say, a hundred channels. With speech synthesis we could make that into 500 channels. But every time we had something working and talked to our counterparts in development at Holmdel like Jake Schaefer and others, they didn't need it. They had another transistorized transatlantic cable, communication satellites and then they had fiber optic cables. So they never needed the bandwidth saving that we offered them. Today speech synthesis is coming into its own for information services, as when a computer talks to you. This is an offshoot of the work that we did in the '50s and '60s.

Nebeker:
But that wasn't the intention at the time?

Schroeder:
Well, it was not just bandwidth compression. Another reason we were interested in speech synthesis was to read documents, as in reading machines for the blind. Optical scanners were already in existence in the '60s, but it was not easy to get speech from such devices. We wanted to do that, even if that was not immediate telephone business.

There was a beautiful application by Western Electric, for the guys who wire these complicated circuits. Here's a complicated circuit chart. In wiring it, they would often solder a wrong connection. So someone wrote an automatic program that translated the wiring chart into a code that we translated into spoken instructions. The wiring man at Western Electric used earphones. He never had to turn his eyes off what he was doing. The earphones would tell him to connect the green wire to terminal 47, that kind of thing. That was, I think, the first application of synthetic speech within the Bell System. It was done in the '60s and supervised by Jim Flanagan who had succeeded me as head of acoustics research in 1963. Over the years Jim and I have collaborated on many projects, including some sophisticated underwater signal processing in Bermuda for the US Navy. Jim later became Vice-President of Engineering at Rutgers University.

We knew that there would be other interesting applications of synthetic speech. Our original purpose of reducing the bandwidth, or data rate, for speech is finally coming into its own with mobile communication, because you can't use optical fibers. You have to go through the air, and eventually there will not be enough frequency space, so you will have to use speech compression. The same is true for the Internet. Also, this compression business got applied to music. Today you see music compression all over the place, in a CD ROM, the World Wide Web and so forth. Everything is compressed now.

Nebeker:
Right.

Schroeder:
Whenever you have expensive storage or whenever there is not enough frequency space, these methods come into their own. Today that's a very active field. In the '60s we did all these things, and nobody was much interested.

Nebeker:
How long did you work on speech synthesis?

Schroeder:
From almost my first day at Bell Labs in '54 to my last day, which was in '87. Thirty three years, to the day. As I said, I worked on many other things. After 15 years I became a professor in Germany and commuted to Murray Hill. That is, I spent five months every year here at Bell Labs and the rest of the time teaching in Germany.

Nebeker:
So from '54 until '69 you were at Bell Labs full time.

#### Management positions

Schroeder:
Yes. I became head of acoustics research in 1958, and in January 1963 I was appointed director of acoustics and speech research. I don't think there were any other immigrants who after eight years in this country were already a research director. Then in '64 I was also put in charge of what was called mechanics research under Warren Mason and Jeff Courtney Pratt. At that point I was in charge of everything that had to do with sound: speech, hearing, room acoustics, ultrasonic, and so forth.

Nebeker:
Did you welcome this management position?

Schroeder:

Nebeker:
Sure.

Schroeder:
He was executive director of communications principles at that time. I had learned from him that whenever there was trouble, you immediately informed your boss, as he had always immediately informed Bill Baker, the vice president, if there was any trouble. (This was so different from the culture that I had experienced in Germany where telling the truth could be fatal. And in the end, it was precisely that culture which proved the undoing of both Wilhelminian Germany and the Third Reich.) So I explained the whole thing and John said, "Well, Manfred, what are you going to do?" I said, "Nothing of course." And John said, "Right!" I didn't leave my office for the next hours, didn't do anything, and of course the thing got boring after everybody had seen the posters. I never saw the posters myself, because I made a point of never going to that floor.

Nebeker:
Even in those management positions you had enough time to do your own research?

Schroeder:
Yes. During my entire life I have always wanted to do what I was interested in—whether I was a pupil in high school or doing my thesis or working at Bell Labs—and I found ways of keeping the administrative load to an absolute minimum.

I will give you another example. Every year someone came down from AT&T, when next year's budget had to be estimated. My colleagues, the other directors, took a day or two—I don't know how long—going through zillions of figures, planned expenses, personnel raises, costs for batch computing, and what have you. It took a long time. I was not interested in doing anything that I didn't find interesting, and I didn't find that interesting. Also, I knew that these projections were all wishy washy anyhow. So before the person from the AT&T budget department arrived, I had on each line a projected figure that I drew out of a hat. They were more or less random. When the guy came in, I said, "Well, I have worked long hours until I came up with these figures." Half an hour later the budget for my area was done, and it was probably as good as all the other budgets.

Nebeker:
You knew that the figures could be changed in the course of the year?

Schroeder:
Well, I figured that AT&T’s money was best spent by my thinking about something interesting, such as speech processing or computer graphics. Then one year the research department was about \$500,000 short, and we were approaching the end of the year. (That is equivalent to about two to three million now.) This meant that the vice president of research had to cough up the money. He called his executive directors: Sid Millman, John Pierce, and Ed David (Bob Lucky I guess came later). They had to absorb that budget shortfall. It may have been \$250,000 that John Pierce had to absorb of the shortfall. So Pierce calls me, and I take a quick look at my numbers and say, "Look, John, you can have \$88,000 from me. I can foresee that I have \$88,000 that I can spare, but don't call me back. You have \$88,000 from me, and that's it." With all this budgeting, they had misjudged the accounts quite substantially.

Nebeker:
Did you actually have money you could forgo?

Schroeder:
Yes, and the reason is that in 1964 we were beginning to buy smaller computers for on line research. Before that we used mainframe computers doing batch processing, machines from IBM, General Electric, and so forth. Then we began using small machines from DEC and Honeywell for on line speech and hearing research. Much of our batch processing was shifted to the smaller machines that we owned.

Incidentally, we had a hard time getting these minicomputers. Bill Baker said, "Look Manny, you know we spent all that money on the big machines, and now you want all these smaller machines." I said, "But this is a completely different thing." We demonstrated for the management the online use of these small computers for speech research or whatever. I still remember Bill Baker saying, "Manny, we are grateful for your having insisted." That is, he saw that you needed big computers and small computers. This was in 1964. We were probably pioneers in the use of small computers. Not so much me personally, but some of my department heads, especially Peter Denes; they saw the need and I supported them. In my budget figures—the pseudo random figures—I had always kept the dollar amount for batch computing, even adding a few percent, even though I knew that we were moving in the direction of small, dedicated computers. The \$88,000 that I could volunteer at that point was from the batch computing that I didn't need anymore.

### Research career highlights

#### Vocoders

Nebeker:
Can you summarize your work in speech research? What are the highlights?

Schroeder:
One early highlight was the following. The main problem with synthesizing not just intelligible speech, which we could do, but natural sounding speech had the so called pitch problem, extracting the fundamental frequency from telephone quality—pardon the expression—speech signals. In about 1955 John Pierce asked me to use Homer Dudley's vocoder principle, not to compress the bandwidths of telephone speech so you could send five times as many conversations over a transatlantic cable, but to take a high fidelity speech signal with a bandwidth of 10 kilohertz or more, compress that down to 3 kilohertz, and send it over regular telephone channels. In other words, send high quality speech over regular telephone channels. That was what John Pierce asked of me. His idea was another application of Dudley's vocoder.

I said, "John, you want to send something that's better than telephone speech, and we have this pitch problem. How can we ever get something better if we can't solve the pitch problem?" Well, it was quite clear it couldn't be solved. So my idea was to take a so called baseband speech signal up to 2 kilohertz, then synthesize the rest from 2 kilohertz to 10 kilohertz by Dudley's vocoder method, and circumvent the pitch problem by generating the higher harmonics from applying a very severe nonlinear distortion to the baseband.

So you transmit the baseband from 300 to 2000 hertz. At the other end you would take the baseband, distort it non linearly to generate frequencies up to 10 kilohertz, and then vocoder fashion give them the right amplitude. This thing was christened “voice-excited vocoder by Ed David.” (David later became Science Advisor to the President with an office in the White House.) The idea came from John Pierce, the name came from Ed David, but the invention of a voice-excited vocoder was mine.

Everybody was flabbergasted. Pierce said, "Manfred, that's the first vocoder that sounds like a human!" Yes, because it had the natural intonation. What makes human speech sound so natural is the intonation pattern and not the buzzy kind of synthetic speech that you usually hear. That was a real breakthrough, and so shortly after that I was put in charge of all acoustics research.

Then came the vocoder work, which, as I had indicated, was a kind of a drag because whatever we did nobody outside research was really interested.

#### Distinguishing between nuclear bomb tests and earthquakes

Schroeder:

Then in about 1965 there were negotiations in Geneva for a nuclear test ban treaty. The head of the scientific delegation was James B. Fisk, president of Bell Labs. An important question was "How can we distinguish between nuclear bomb tests and earthquakes?" Atmospheric tests had already been banned under Kennedy, and now they wanted to ban underground tests. Someone called John W. Tukey—you must have heard his name...

Nebeker:
Of course.

Schroeder:
Tukey and Bruce Bogert invented this cepstrum. I was very close to Tukey, so I had heard about the cepstrum very early on. The cepstrum is a method that allows the measurement of differential delays so that you could distinguish between a surface nuclear explosion and a deep mantle earthquake. The delay pattern of reflections from the earth's core and mantle would be completely different in the two cases. It was for that purpose—for Fisk and for the U.S. side in these negotiations—that John Tukey invented the cepstrum. I heard about this almost immediately, and I said, "Wait a minute. That's our pitch problem. Let's not call it fundamental frequency, let's call it fundamental pitch periods, from one flap of the vocal cords to the next. That's really what we want to measure." So I said, "Let's apply Tukey's cepstrum method to the pitch problem," and I assigned a summer student, A. Michael Noll, to the problem.

Nebeker:
I know of his writings.

Schroeder:
He was the only person from a development department that we hired in research. It was the summer of 1962, and I had to go to a meeting in Europe. Mike Noll appeared as an exchange student from Frank Andrews' department in development. I said, "Mike, here is this idea of Tukey's, the cepstrum. Try that on speech. It must work." I came back a couple of weeks later from Europe, and Mike Noll had solved the pitch problem using Tukey's cepstrum and became famous for it. That was another highlight.

#### Computer graphics

Schroeder:

Later Mike, Bela Julesz and I, stimulated by Leon Harmon, became interested in computer graphics for artistic purposes. I once even won First Prize at the International Computer Art Exhibition in Las Vegas in 1969 with an image of a human eye that was entirely composed of letters. Using the same technique I designed the poster for the Brooklyn Museum show "Some More Beginnings—Experiments in Art and Technology." (The poster showed the entrance to the museum composed of text announcing the show.) I was greatly helped in my computer graphics, and signal processing in general, by several superb programmers, especially Sue Hanauer and Lorinda Landgraf Cherry.

#### Speech recognition

Schroeder:

We did almost no work on speech recognition during those years in the '60s because John Pierce didn't believe in it. That research was practically cut off. It was revived only when Pierce was retired in 1972 and went to Caltech, or rather the Jet Propulsion Laboratory and Caltech. Later he went to Stanford. He became chief scientist—or some such title— at the Jet Propulsion Laboratory, and he was also a professor at Caltech. So John Pierce had to leave before the speech recognition work would resume. He was dead set against it.

Nebeker:
Were you interested in pursuing it?

Schroeder:
I must admit that I was not much interested either. You see, even if John Pierce was against it, if I had put my foot down and said, "Look, this is important and we can do it," we would have done it. But I didn't believe in it myself either.

Nebeker:
In retrospect do you think it would have been good to continue that work?

Schroeder:
Yes, I think we should have pursued it more actively. However, we did some interesting work on talker identification that was helpful in the investigations of several disasters such as the mid air collision of two airliners over the Grand Canyon in 1956 and the burning up of three Apollo astronauts on the ground. We were able to identify the voice of who screamed first “Fire, fire; we are burning up!” That helped NASA to pinpoint the source of the original fire. This was a difficult job both psychologically, because these were the last words of a burning human being, and because the voice sounded like that of a screaming child so we had to ignore the pitch and rely on other cues.

#### Speech synthesis

Nebeker:
You continued to work on speech synthesis.

Schroeder:
Yes. I focused on speech synthesis, and then came the biggest highlight of them all in speech synthesis. In 1966 I was walking up and down my office with Bishnu S. Atal there, whom I had hired in 1961 from India. He had the highest recommendations from India. Dick Bolt had told me about him, that there was this smart Indian student called Bishnu Atal. So I contacted him, and ever since he came to Bell Labs—it was in 1961—we have worked on speech together.

That day in 1967 I was pacing up and down my office, saying, "We have to do something about the vocoder speech quality." We had solved the pitch problem with the cepstrum method, but it still didn't sound right like a real human voice. The trouble in a vocoder was that we went on the basis of a fixed and inflexible paradigm. We needed to code speech so as to leave room for error. From this conversation with Bishnu evolved the idea of predictive coding.

The idea is the following. As speech is being encoded, continuously predict, on the basis of preceding samples, the subsequent speech samples; compare the prediction with the actual speech; and transmit the prediction error, which is called prediction residual. In decoding, use of the same prediction algorithm and knowledge of the prediction residual allow accurate reconstruction of the actual speech.

Well, that idea, which we called adaptive predictive coding, turned out to be absolutely marvelous. The idea was already in existence for television picture coding, but those coders were fixed. With speech we needed predictors that changed with every speech sound, and to make that clear we called this adaptive predictive coding, APC. We wrote a paper for the Bell System Technical Journal and presented the technique at WESCON, a major IEEE conference, in 1967. Some Japanese also discovered it, but happily somewhat later.

The quality was just like my voice excited vocoder in the '50s. It was wonderful. It really sounded like natural speech. As you know, we later changed the name to linear predictive coding; LPC, and that really took off. In the early '70s the digital integrated circuits came along. Some of the coding that we had envisioned was so complex that people said we could never implement it. I said I didn't care; I was interested in creating synthetically on the computer a speech signal that cannot be distinguished from the natural human voice. I felt that sooner or later people would come up with the necessary hardware. Sure enough, today these coders fit on a little chip.

Nebeker:
Yes.

Schroeder:
The reason I pursued this was that I thought it was interesting, and I didn't care whether it could be done in the real world or not. However, I was confident that might happen eventually. In fact, the development in hardware was much faster than we had imagined.

One thing that made predictive coding so complicated to implement was that in 1973 I had the idea of not minimizing the noise power, the RMS (root mean square) noise, but the loudness of the quantizing noise. The prediction residual gets quantized, so you have quantizing noise. In the original LPC the noise power is minimized. But no, I knew enough about hearing to realize this was wrong. The ear doesn't care about power, the ear cares about loudness, which is a very complicated function of the actual spectrum. So we want to minimize the loudness of the quantizing noise. That resulted in a very complicated algorithm, which again nobody thought could ever be implemented. Now everybody does it. People even forget who had the idea originally. Everybody is using what they call noise weighted speech coding, and it all fits on a little chip.

In the meantime I took the Göttingen position and spent only part time at Bell Labs, but the close cooperation with Bishnu continued. We have about ten joint papers, mostly Atal Schroeder, or Schroeder Atal, on LPC, on noise weighted coding for LPC, and so forth. This kind of LPC has since become a government standard. I mean I am so happy that after working for 15 years on speech when nobody was interested, finally the things we did in the '70s are taking off like a rocket. The first applications I remember were the Texas Instruments "Speak & Spell" or little dogs that would talk or talking cameras. Now it would be difficult to imagine a world without speech synthesis. And when we say speech synthesis it's almost always LPC based.

Nebeker:
Did you patent this work?

Schroeder:
Yes, it was of course patented. At one point we discovered the Japanese were doing practically the same thing that we did. I am not talking about basic LPC, which they invented independently. That was really independent, with a completely different approach but resulting in the same thing—Itakura and Saito at NTT. But in the '70s when Atal and I were doing these more sophisticated things, like error weighting and noise weighting, the Japanese were doing a very similar thing without paying any attention to our patents. So of course the patent lawyers got into it. The Japanese claimed, "This is different and this is different and this is different; we're not doing the same thing." You know a patent is not an absolute thing.

Nebeker:
Sure.

Schroeder:
What the actual royalty situation is today, I have no idea.

Nebeker:
Were all these patents owned by Bell Labs?

Schroeder:
Well, pretty soon, beginning in the middle 1970s say, it became so generally the method of choice that many other companies, especially in the U.S. and Japan, were using LPC and getting patents for how to encode these so called slowly varying parameters. Who has which patents at this point and how many there are, would be a major study. Certainly the basic patents were owned by Bell Labs.

#### Hearing

Nebeker:

Schroeder:
As I said, vocoder speech had a kind of rough quality. One aspect of my work in hearing that applied directly to LPC concerned the extent to which noise masks the sound you are trying to hear.

I started a research project with Joe Hall. We started work on the masking of noise by tones. The results of that were then applied to linear predictive coding, with the aim of making the quantizing noise as inaudible as possible, minimizing the loudness of quantizing noise. But basic knowledge about hearing that goes into this work was not available in 1973 when we started this. That was work in hearing that was related to speech research, but that was at a late stage.

At an early stage—in about 1956—I was bothered by the rough quality, the buzzy quality, of vocoder speech. I thought it had something to do with the phase spectrum of the signal, not just the amplitude spectrum but the phase spectrum. So I did quite a bit of work in pure hearing research on the so called monaural phase sensitivity. I discovered that if you take a wide band signal, a periodic signal, let's say 31 harmonics at 100, 200, 300 hertz, up to 3100 hertz, and if they are all in phase, you get a periodic pulse that sounds very buzzy, just as it looks on a scope. But then if you randomize the phases, you get a soft sounding period signal. I thought that would be good to synthesize voice, speech not from pulses but from phase randomized signals. That was my first encounter with hearing research influencing speech research—this work on monaural phase sensitivity.

Nebeker:
The hearing research sounds more like traditional biophysics research. You are trying to understand human perception itself.

Schroeder:
Yes, you might call this work on monaural phase sensitivity basic research in hearing, while the work on the masking of quantizing noise was application directed.

Nebeker:
Right.

Schroeder:
I did one more basic thing with Joe Hall on a mathematical model of the hair cell, the receptor organ in the human inner ear, which translates mechanical vibration on the basilar membrane in the inner ear into electrical impulses that then go to the brain. We wanted to have a good mathematical model, and Hall and I proposed one. But on the whole, I didn't do that much in hearing. It wasn't my main field, but nevertheless there were some things I did.

Nebeker:
You said earlier on that your research was in three areas.

#### Room acoustics

Schroeder:
The third one was room acoustics, my old field from my Ph.D. thesis. That was reactivated in connection with work on Philharmonic Hall in 1963 at Lincoln Center for the Performing Arts in New York City. The acoustics there were severely criticized, and the management of Lincoln Center turned to AT&T. AT&T turned to Bell Labs, and then Bill Baker asked me to join a committee of four experts to look at the acoustics situation at Philharmonic Hall. The other three were consultants, but I, by the consent decree between Western Electric and the government, was not allowed to do consulting. But I was permitted to make measurements and assess the situation.

So I had the opportunity to reenter my old field of concert hall acoustics and, with Gerhard Sessler and Jim West, to develop a number of new signal processing methods for making measurements in concert halls. There was also an immediate interest at Bell Labs and AT&T. As I mentioned earlier, we were starting, in the 1960s, to think seriously about conference telephony and speakerphones, where of course room acoustics becomes important.

I then did quite a bit of work in room acoustics, developing new methods, computerized methods, of measuring reverberation time and a better theory of reverberation, based on an integral equation. Of course we couldn’t solve the integral equation and I asked Dave Slepian to look into the problem. He brought along Ed Gilbert who, within a day, came up with an iterative method that worked exceedingly well. We thus made a substantial contribution to the efforts to salvage Philharmonic Hall.

Other Bell mathematicians who, over the years, have helped me a lot and whose friendship I have treasured are Jessie MacWilliams, Andy Odlyzko, Neil Sloane, Ron Graham, Henry Landau, Larry Shepp, Colin Mallows, Aaron Wyner and Jeff Lagararias. I also remember some of the “old guard”, especially Hendrik Bode, Harry Nyquist, S. O. Rice and Serge Schellkunoff.

I have seen relatively little of Claude Shannon because he was already half gone from Bell Labs when I joined. He once appeared in my office with a trumpet whose normal modes he wanted to know. And I always liked demonstrating his Outguessing Machine (built by David Hagelbarger) to VIP visitors (Friedrich Hirzebruch for one).

Nebeker:
It's interesting to me that your theoretical early work was relevant to practical problems of different sorts.

Schroeder:
Yes.

### Göttingen faculty position

Nebeker:
Could I quickly get the story of your Göttingen career?

Schroeder:
One of the first things I did at Göttingen was to get money from the German Science Foundation for a major study of concert halls around the world. At that time—this was 1970—they had enough money, so we measured 22 halls, mostly in Europe. The London Chamber Orchestra had provided us with a recording of reverberation free music recorded in an anechoic environment. These tapes were radiated from loudspeakers on the stage of these different concert halls, and we made recordings with an artificial head. Together with Atal, in the '60s, I had developed a method of reproducing such recordings in an anechoic room, so you would have the impression of actually sitting in the concert hall. We then had dozens of listeners evaluate these: make AB comparisons and use multidimensional scaling methods developed by Joe Kruskal, Doug Carroll, Roger Shepard and others at Bell Labs.

We found that the major deficiency in modern concert halls was the lack of early lateral sound, reflections from the sidewalls. Modern halls are built with a low ceiling because they are air conditioned— you don't need the air up there to breathe— and they are built fairly wide because you have larger audiences and people themselves are somewhat wider now. The result is that the beneficial lateral reflections from the far sidewalls come very late and are very weak. But you get a strong reflection from the ceiling, which carries a monophonic sound. If you look towards the stage, most of the sound from the stage and the strong ceiling reflection give you a monophonic signal. Putting it in a nutshell, this project, which resulted in four or five Ph.D. theses over several years, showed that there is too much monophonic sound in a modern hall with the low ceiling and wide seating area.

Nebeker:
I see. What position were you offered at Göttingen?

Schroeder:
I became professor of physics and director of the Third Physics Institute, an experimental institute.

Nebeker:
The offer was made in 1969?

Schroeder:
Yes, and I accepted it. I had been a director at Bell Labs for more than six years, and the only way up would have been executive director and more administration, which I didn't like. In any case I thought this would be an interesting challenge, and it was a challenge to teach.

Nebeker:
You must also have been attracted to the German setting.

Schroeder:
Yes, it was a kind of homecoming for me. But it was difficult for the family. The children didn’t speak any German to speak of, and there were any number of logistic and social problems— the shopping, everything was more difficult. But as far as I was concerned, I was settling in a well prepared nest (I'm translating a phrase from German).

I'll give you one story, again illustrating my outrageous approach of administering things. When I was there negotiating my budget, there was one item there called Prozessrechner. I said, "What's that?" It was what you call an on line computer. I said, "Two hundred thousand marks for an on line computer? That's not enough." Now I didn't want the secretary to retype that whole list that I was to take to the government, so I said, "Just type a 1 in front, and make it 1.2 million." Later, in fact, it turned out to be 2.3 million.

Then I wanted to put the computer in a certain hall there. It turned out that hall was not big enough, that we needed an additional building, an annex. So I called the chief administrative officer, the chancellor of the university, and said, "Look, we need this extra building." He said, "Do you have the money for it?" No, I didn't because I had planned to put it in that hall that wasn't big enough. But I said, "Yes, of course I have the money." I put the receiver down and immediately called the head of the government department. I explained, "Look, so and so happened. I never thought that I would need this building, so of course it wasn't on my list, but when I talked with the chancellor I told him I have the money. Of course, I don't have the money." You know what the guy in the government said? He said, "You have the money." The building was built. That couldn't happen today. This was 1970.

Nebeker:
So at Göttingen you were teaching and administering this institute?

Schroeder:
Yes, and supervising students.

Nebeker:
Doing research as well, I imagine.

Schroeder:
Yes. This study of the 22 concert halls had an interesting coda. Namely, how do you build a new concert hall that doesn't have these problems that I mentioned before (mainly, too much sound from the top and not enough sound from the sides)? Well, you could leave off the ceiling, but then when it rains everybody gets wet.

My thought then was that we need a ceiling that doesn't reflect the sound specularly, that is, like a mirror, but rather in a diffused, wide pattern. Being a crypto mathematician, I saw that we needed a reflection phase grating—that's of course a physicist’s term—a structure on the ceiling that has this property of diffracting equal amounts of energy to all different directions.

Now that is a mathematical problem. I knew that number theory would hold the answer to this problem. I invented several number theoretical surface structures that have this property: if you hit it with a wave, the wave will be reflected in a very wide pattern. I got so deeply into number theory because of this concert hall problem and got so many ideas for other applications that I wrote a whole book, Number Theory in Science and Communication, that became a best seller.

The first of these installations was in Wellington, the capital of New Zealand. Several number theoretic surfaces were installed. Companies were formed in this country and abroad, called Reflection Phase Gratings, Incorporated, and so forth. The surfaces made their way into homes. Forbes magazine sent a reporter out to individuals, asking them, "What's that over there in the corner of your living room?" The guy says, "That's a Schroeder box." "What's a Schroeder box?" "I don't know, but it's called a Schroeder box." "What does it do?" The guy says, "It makes the wall disappear," which I found a wonderful quote.

You see, if you put one of these surfaces they call Schroeder boxes against a bare wall, incoming sound gets widely dispersed so you don't get a harsh echo. The manufacturers of these surfaces, officially called reflection phase gratings, or quadratic residue gratings, got churches and lecture halls and even private individuals to buy them.

You asked me about patents before. I never patented those gratings. By that time, the mid 1970s, I had 45 U.S. patents and many more foreign ones. It's always a lot of work to write a patent. An attorney actually does that, but it's still a lot of work. So I never patented the gratings. I just published it, putting it in the public domain. Later I saw my chief patent attorney, Al Hirsch, and said, "Al, didn't I make a mistake? Everybody is manufacturing this, and AT&T didn't get a patent out of it." But Hirsch said, "No, if you had proposed it as a patent, we would probably not have acted on it. We would have thought, in 1975, that it was only a small item." You know, filing a patent is very expensive, with the attorney's time and the filing fees. He said, "Please be assured you didn't make a mistake."

### The importance of mathematics

Nebeker:
I see that we have to stop. Can you summarize some of your experiences?

Schroeder:
I have often asked myself why so many people loathe mathematics. Of course I always found it easy. But I don’t think that is the whole story. There is a kind of “macho” culture that proclaims mathematics difficult and completely ignores the beauty of it. This ill omen is perpetuated by teachers who don’t know how to make mathematics, one of the most interesting subjects, interesting. We need more people like Martin Gardner, John Horton Conway and Ron Graham who have given ample proof that mathematics is great fun (and occasionally outright funny).