# Oral-History:Tom Parks

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There was a Princeton conference that goes on, every other year. It’s at Johns Hopkins on alternate years. I don’t know the exact name of it, but it's in March. I don’t know whether that was the same year as the Arden House in ’70 or ’71. But that is where the Parks-McClellan algorithm was invented by Parks and McClellan actually. [[Oral-History:Hans Wilhelm Schuessler|Schuessler]] wrote a paper on design of equiripple filters. He and Otto Herrmann wrote down the conditions for an equiripple filter and how many ripples there had to be. They had a pretty straightforward way to solve the equation, to get the coefficients for these equiripple digital filters. Ed Hofstedter gave a talk at the Princeton conference on a faster way to solve [[Oral-History:Hans Wilhelm Schuessler|Schuessler's]] equations. It was an exchange algorithm. The problem with [[Oral-History:Hans Wilhelm Schuessler|Schuessler's]] equations was that they were written down so that you made sure the error was the same. It was equal height ripples. But you didn’t know where the ripples would occur. You didn’t know which frequency would have the peak values. So what Ed Hofstedter did is he started with some initial frequencies and then iterated the frequencies and tried to find the frequencies where the peaks were in the error. During his talk, I thought that sounded like the Remez exchange algorithm. Jim Thorpe had taught a course at Cornell on Approximation Theory. I think it was EE5670. So I had learned about the Remez exchange algorithm from Thorpe and I continued to thank him for teaching me that because it looked like Ed Hofstedter was doing the Remez exchange algorithm. Except it was slightly different because Ed was solving [[Oral-History:Hans Wilhelm Schuessler|Schuessler's]] equations which were the constant height errors. The Remez exchange allows the error to get bigger on every iteration. So I went up afterwards and asked Ed, “Isn’t that the same as the Remez exchange algorithm? Is that what you are doing?” And he said, “Well, maybe it is.” I think that he knew about the Remez exchange algorithm and I said, “Well, why don’t you just solve the problem directly using the Remez exchange?” And he said, “Well, I don’t know. It’s not what [[Oral-History:Hans Wilhelm Schuessler|Schuessler]] wrote down. [[Oral-History:Hans Wilhelm Schuessler|Schuessler]] wrote down these other equations, and I was finding a fast way to solve Schuessler's equations.” Which he did. I think [[Oral-History:Alan Oppenheim|Al Oppenheim]] was working on the problem too at the same time. I think that Al might have written a conference paper on equiripple filter design. I think Ed Hofstedter was at Lincoln, MIT Lincoln Lab. I believe that Al might have been working with him. Anyway, Ed said, “Yes, it probably is the Remez exchange algorithm.” So I went back and he said, “Might be a good thing to work on.”

There was a Princeton conference that goes on, every other year. It’s at Johns Hopkins on alternate years. I don’t know the exact name of it, but it's in March. I don’t know whether that was the same year as the Arden House in ’70 or ’71. But that is where the Parks-McClellan algorithm was invented by Parks and McClellan actually. [[Oral-History:Hans Wilhelm Schuessler|Schuessler]] wrote a paper on design of equiripple filters. He and Otto Herrmann wrote down the conditions for an equiripple filter and how many ripples there had to be. They had a pretty straightforward way to solve the equation, to get the coefficients for these equiripple digital filters. Ed Hofstedter gave a talk at the Princeton conference on a faster way to solve [[Oral-History:Hans Wilhelm Schuessler|Schuessler's]] equations. It was an exchange algorithm. The problem with [[Oral-History:Hans Wilhelm Schuessler|Schuessler's]] equations was that they were written down so that you made sure the error was the same. It was equal height ripples. But you didn’t know where the ripples would occur. You didn’t know which frequency would have the peak values. So what Ed Hofstedter did is he started with some initial frequencies and then iterated the frequencies and tried to find the frequencies where the peaks were in the error. During his talk, I thought that sounded like the Remez exchange algorithm. Jim Thorpe had taught a course at Cornell on Approximation Theory. I think it was EE5670. So I had learned about the Remez exchange algorithm from Thorpe and I continued to thank him for teaching me that because it looked like Ed Hofstedter was doing the Remez exchange algorithm. Except it was slightly different because Ed was solving [[Oral-History:Hans Wilhelm Schuessler|Schuessler's]] equations which were the constant height errors. The Remez exchange allows the error to get bigger on every iteration. So I went up afterwards and asked Ed, “Isn’t that the same as the Remez exchange algorithm? Is that what you are doing?” And he said, “Well, maybe it is.” I think that he knew about the Remez exchange algorithm and I said, “Well, why don’t you just solve the problem directly using the Remez exchange?” And he said, “Well, I don’t know. It’s not what [[Oral-History:Hans Wilhelm Schuessler|Schuessler]] wrote down. [[Oral-History:Hans Wilhelm Schuessler|Schuessler]] wrote down these other equations, and I was finding a fast way to solve Schuessler's equations.” Which he did. I think [[Oral-History:Alan Oppenheim|Al Oppenheim]] was working on the problem too at the same time. I think that Al might have written a conference paper on equiripple filter design. I think Ed Hofstedter was at Lincoln, MIT Lincoln Lab. I believe that Al might have been working with him. Anyway, Ed said, “Yes, it probably is the Remez exchange algorithm.” So I went back and he said, “Might be a good thing to work on.”

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Yes, all of a sudden. That was great. Then another great thing that happened was that I had a sabbatical coming up in ’73, and [[Oral-History:Hans Wilhelm Schuessler|Schuessler]] invited me to Germany on the Humboldt program because he had been my master's thesis advisor. I went over there and on the way I spent the summer at Lincoln Lab, and worked for [[Oral-History:Ben Gold|Ben Gold]]. My wife is from the Boston area. I do all of these things for the wrong reasons, not planning my career, but she grew up in Beverly, Massachusetts, near Boston. We thought that it would be fun to stop there during the summer.

Yes, all of a sudden. That was great. Then another great thing that happened was that I had a sabbatical coming up in ’73, and [[Oral-History:Hans Wilhelm Schuessler|Schuessler]] invited me to Germany on the Humboldt program because he had been my master's thesis advisor. I went over there and on the way I spent the summer at Lincoln Lab, and worked for [[Oral-History:Ben Gold|Ben Gold]]. My wife is from the Boston area. I do all of these things for the wrong reasons, not planning my career, but she grew up in Beverly, Massachusetts, near Boston. We thought that it would be fun to stop there during the summer.

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Germany was great. Then I came back and [[Oral-History:James W. Cooley|Jim Cooley]] came to Rice and gave a talk. He said to me, “You might want to look at the National Academy. There is a paper in there that you might find interesting…” It was a paper on computational complexity of convolution and FFT algorithms, and Jim wasn’t really allowed to tell me much about it, because IBM wanted to keep it a secret but still wanted to publish it somehow. I tried to read it, and I couldn’t read it. So I had a really good student Dean Kolba who was interested in it, and so we spent the whole summer reading this paper. It was based on some of the number theory ideas that I had learned in working with [[Oral-History:Charles Rader|Charlie Rader]] and Irving Reed, the year before. So over the summer Dean Kolba and I finally managed to understand what it was and we published a paper on it.

Germany was great. Then I came back and [[Oral-History:James W. Cooley|Jim Cooley]] came to Rice and gave a talk. He said to me, “You might want to look at the National Academy. There is a paper in there that you might find interesting…” It was a paper on computational complexity of convolution and FFT algorithms, and Jim wasn’t really allowed to tell me much about it, because IBM wanted to keep it a secret but still wanted to publish it somehow. I tried to read it, and I couldn’t read it. So I had a really good student Dean Kolba who was interested in it, and so we spent the whole summer reading this paper. It was based on some of the number theory ideas that I had learned in working with [[Oral-History:Charles Rader|Charlie Rader]] and Irving Reed, the year before. So over the summer Dean Kolba and I finally managed to understand what it was and we published a paper on it.

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Well, I worked on time frequency analysis. That was something I had started working on at Rice, just before I left. Faye Boudreau was a Ph.D. student of mine at Rice. Then, I continued to working on that at Cornell, and had a very good student Ram Shenoy. He was the top of his class at Cambridge. He is still a very great contributor and mathematician. He did a lot of good work in his Ph.D. thesis on time frequency analysis, group theory, group representation theory. I have been working on things like that in addition to multi-rate systems ever since.

Well, I worked on time frequency analysis. That was something I had started working on at Rice, just before I left. Faye Boudreau was a Ph.D. student of mine at Rice. Then, I continued to working on that at Cornell, and had a very good student Ram Shenoy. He was the top of his class at Cambridge. He is still a very great contributor and mathematician. He did a lot of good work in his Ph.D. thesis on time frequency analysis, group theory, group representation theory. I have been working on things like that in addition to multi-rate systems ever since.

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We’ll check it out. Thank you for the interview.

We’ll check it out. Thank you for the interview.

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## Contents

Tom Parks was born March 16, 1939 and grew up in Buffalo, New York. He majored in electrical engineering for his bachelors at Cornell, and while there he worked at the Cornell Aeronautical Lab in Buffalo on magnetic amplifiers and designing circuits, developing an early interest in analog signal processing. Parks went to GE in Ithaca to work on telemetry, and later returned to Cornell for his masters and PhD working with Hans Schuessler and Jim Thorpe. After graduation, he was hired at Rice University and while there he began studying digital filters. His interest in number theory transforms came with a stint at the Lincoln Labs under Ben Gold in 1973, while in the 1980s Parks did consulting work for the Schlumberger in Houston where he became acquainted with acoustic well logging and associated signal processing. He returned to Cornell to teach in 1986, where he continued his work from his time at Rice on time frequency analysis, but also work on multi-rate systems.

In the interview, Parks discusses the building up of signal processing departments at Rice and Cornell, and his teaching of a DSP course in 1969 or 70. He details the inspiration for and work on the Parks-McClellan algorithm with Jim McClellan, and his winning of an IEEE paper award on a paper co-written with Dean Kolba on computational complexity of convolution and FFT algorithms. Parks also talks about his ideas on building theory in order to create more research opportunities.

Parks summarizes key developments in the field of digital signal processing. For further discussion of these events, see James W. Cooley Oral History, Ben Gold Oral History, James Kaiser Oral History, Wolfgang Mecklenbräuker Oral History, Russel Mersereau Oral History, Alan Oppenheim Oral History, Lawrence Rabiner Oral History, and Ron Schafer Oral History.

TOM PARKS: An Interview Conducted by Frederik Nebeker, IEEE History Center, 14 May 1998

Interview #342 for the IEEE History Center, The Institute of Electrical and Electronics Engineering, Inc.

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, 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:

Thomas Parks, an oral history conducted in 1998 by Frederik Nebeker, IEEE History Center, New Brunswick, NJ, USA.

## Interview

Interview: Dr. Tom Parks

Interviewer: Frederik Nebeker

Date: 14 May, 1998

Place: Seattle, Washington

### Childhood and education

Nebeker:

You were born 16th of March 1939. Can you tell me a little about your family?

Parks:

Well, my father was an electrical engineer. He went to RPI and was an electric power sales man. My mother was a nurse. She went to nursing school in Rochester. They lived in Buffalo for a long time.

Nebeker:

So you grew up in Buffalo?

Parks:

I grew up in Buffalo.

Nebeker:

Parks:

I didn’t think so. In fact, he wanted me to go to RPI. I can still remember, I was trying to decide where to go to college, and he drove me to RPI. I don’t know if you have ever been to RPI, but especially in the rain, it’s kind of a dismal, bleak looking place. The campus is right next to some run-down area. I refused to get out of the car. I can remember how mad he was. I just didn’t like the look of RPI. My father got me a summer job being an electrician's helper at a power plant construction project. So I did some power-related electrical stuff. It wasn’t anything to do with what I do for research now, but it was shearing conduit. Maybe there was some influence.

Nebeker:

When you went off to college, was it with the intention to major in EE?

Parks:

Yes, in those days you were required more or less to say what you were going to do early. Now you don’t have to declare your major until later. I went there and signed up for electrical engineering from the beginning.

Nebeker:

And that was Cornell?

Parks:

Yes, Cornell. In those days they would let you in the freshman physics course. You would look to the right and look to the left, and those guys won’t be there when you graduated. It was very competitive the first couple of years. They didn’t leave Cornell, they went to other areas. It was known that electrical and chemical engineering were the two difficult ones and if you were having trouble you could go into civil. If you were still having trouble, you would go to hotel school. It was a five year program then.

Nebeker:

For a bachelor's?

Parks:

For a bachelor's degree, bachelor of Electrical Engineering. The idea wasn’t to have more technical courses, but to have a broader education rather than training. So I took courses in Native American culture, and a lot of other courses that I wouldn’t usually take.

Nebeker:

Oh, I see. So, the EE curriculum is usually so full that you that you don’t have an opportunity to take many others.

Parks:

Yes, Cornell had that five year program for a very long time. A few years after I graduated, they cut back to four. In fact I think, and maybe it's a coincidence, but I went to Rice on the faculty and Rice had also had a history of a five year program. I’m not sure why. I enjoyed it. The five years were fun.

Nebeker:

So, when you finished and received a bachelors degree, had you decided on a branch of EE?

Parks:

Well, I was in the Cornell co-op program and because it was a five year program there were the three assignments in industry: one fall, one spring, and one summer.

Nebeker:

There are a lot of co-op programs that are still five year programs.

Parks:

Yes. It is part of the regular five year program, but it was a co-op assignment. I worked at Cornell Aeronautical Lab in Buffalo and did electronics basically, magnetic amplifiers, designing circuits. So in a way that was signal processing, analog signal processing and radar work primarily. I didn’t have any idea that I was interested in research. I wanted to get out of Cornell. I wanted to go to work. I went to work for GE, in Ithaca.

### GE employment

Nebeker:

What department?

Parks:

They had what they called I think Advanced Electronics Center at the airport in Ithaca. Cornell was trying to build up an electronics research center, and they never did. In fact GE is not there anymore. It was a fun place to work.

Nebeker:

What were you doing there?

Parks:

Telemetry. I guess I just didn’t want anymore theory and school work. So, one of the exciting things about the job was field work. We got to go out to New Mexico and launch balloons with telemetry instrumentation.

Nebeker:

So you were building instrumentations?

Parks:

Well, yes. Sometime more boring things like power supplies. But recording high altitude explosions basically, pressure pulses, and things from high altitude explosions. We carried instruments and the explosive up 100,000 feet or so with a balloon and then set it off over the White Sands missile range.

Nebeker:

This wasn’t meteorology, but just dynamics?

Parks:

No it was called, the project was called BANSHEE, Balloon and Nike Simulated High Explosive Experiment. It was right after the nuclear test ban, and atmosphere testing went into effect. I think that originally they wanted to find the effect of high altitude nuclear explosion. So this was simulation with chemical explosions. It was signal processing again, but it was analog signal processing. Transients pulses had to be recorded without saturating everything.

Nebeker:

How long did you have to work there?

Parks:

I just worked there for two years as a Bachelor's degree engineer. I started taking courses at Cornell because I was still working in Ithaca. I got more interested in Cornell. Probably one of the better things that happened to me was GE decided to leave Ithaca and they gave me a choice of going, to Oklahoma or Syracuse. I thought that was a good time to go back to school full time so I did.

### Graduate studies; signal processing and signal theory

Nebeker:

After you had been out as a practicing engineer, school didn’t seem so bad?

Parks:

Well, school started to be more relevant. I think they had hired quite a few new faculty over those few years. I mean I wasn’t away long. My thesis advisor Jim Thorpe for example had just recently been hired. I had some good people; we were doing some new interesting things. I wanted to try doing some research and went back there full time. And my wife encouraged me. I don’t know how she knew that I would like doing that, but she did. She would say, “You really ought to try going to graduate school and getting a Ph.D.” She was a chemistry major as an undergraduate and I think she wanted to get a Ph.D. herself in chemistry. We had two small children while I was in graduate school. She went on to get her Master's degree, and never got her Ph.D.

Nebeker:

So, in something like ’63 you went back to Cornell full time?

Parks:

Yes.

Nebeker:

And got a master's the next year?

Parks:

Yes

Nebeker:

And what were you studying mainly?

Parks:

For my master's, a lot of interesting chances happened. Hans Schuessler, has been a big influence on signal processing, and upon me in particular. While I was there, he was visiting Cornell for a year. He was my master's thesis advisor.

Nebeker:

How did you choose him, or did he choose you?

Parks:

He was doing some interesting things. Nick Declaris was there and Jim Thorpe had just started on the faculty. Nick Declaris was a faculty member from MIT. They had a lot of new students, and I think Declaris had only recently come there, and they were just starting up a lot of new programs. Maybe Schuessler was just looking for somebody to supervise. But he was doing some interesting things with analog computers.

Nebeker:

Okay, was it analog computers projects?

Parks:

Yes, there was a lot of simulation. I guess the money came from Declaris’s contract. It was a vacuum tube contract from Ford Monmouth. So we had to do something with vacuum tubes. But I built a tapped Ley line pulse-shaping network with vacuum tubes and there was a lot of simulation that had to go on an analog computer. And so that is what Schuessler worked with me on. I mean it was very hard working with him because he was so fast at everything. We would talk about doing something, and it wasn’t clear whether I was suppose to do that, or what. And he would have it done the next day himself. He was just having a lot of fun with a good computer facility there. I think he had gotten his Ph.D. in analog computers. So he was a real expert.

Nebeker:

Do you remember what analog computers he used?

Parks:

I don’t remember. I can remember how thick the cables were, and everything when you were plugging stuff together, but I don’t remember the name of it.

Parks:

So, I got interested in signal processing from him. He was doing analog signal processing again, but still a lot of interesting things with the analog computer. So I kind of liked signal processing already in the analog signal processing stage. We had to get the pulse shape just exactly right for this match filter. And there was a lot of interactions of stray capacitants and things like that all in the simulator. That was practical in building things. Then Jim Thorpe wanted some new students, and he was interested in analog signal processing. There was a lot of interest in some work that Kautz had done as well as McDonough and Huggins. But Huggins had a group at Johns Hopkins that did analog signal processing filters. That was probably the most interesting start I got in signal processing, through reading about it in a lot of their papers. They were doing filter banks which are popular now a days, but they are all analog or Harst  RLC filters.

Nebeker:

As soon as your masters thesis was completed, you started working with Thorpe?

Parks:

Yes, I stayed. in fact, Thorpe was still working with me. I don’t know who was my official advisor. I actually worked with Schuessler. Then Thorpe became my Ph.D. thesis advisor.

Nebeker:

Parks:

Signal theory. It was based on a lot of this work that Huggins did on different ways to represent signals. It looked at ways to choose basis functions to represent signals efficiently. Nowadays it would be called compression.

Nebeker:

So that is kind of a theoretical basis for any sort of signal processing, or specifically analog sort of thing that you were talking about?

Parks:

Most of the equations were integrals and it was pretty general in an inner-product space, a pretty general mathematical setting. But the inner-products involved integrals.

Nebeker:

These were continuous functions that you were dealing with?

Parks:

Yes. I can’t say that I did digital signal processing for my thesis.

Nebeker:

But you did signal theory.

Parks:

In fact, one of my favorite books, Signal Theory by Lou Franks. Although I don’t think that it was around then. I think it was written, in the late ’60s after I graduated. So I would say that my thesis was on signal theories, signal representations.

### Rice employment and teaching

Parks:

I didn’t really start any digital signal processing until I got to Rice. I went to Rice right after my Ph.D. Henry Bourne  hired me. I was interviewing at a lot of places, and fortunately the job market was pretty good for new Ph.D.’s then. I had offers from Wisconsin and RPI. I didn’t apply to MIT. I guess with hindsight, I wish that I had. Maybe MIT would have been the right place to be in 1967. And the offer from Rice was really attractive, because Henry Bourne was creating a new department. He came from Berkeley. His area was magnetics and materials and things and not signal processing. He was a very dynamic, aggressive chairman and hiring a lot of people. The departments were growing rapidly. It was a very attractive place. I think Sidney was hired maybe a couple of years before I was, ’65. He had only been there a year or two.

Nebeker:

There wasn’t much of a graduate program, when he arrived.

Parks:No. Henry Bourne built the whole thing and had pretty sustained hiring. I mean, I appreciate it more now that I have been on a lot of recruiting committees and everything. He didn’t just panic and try to hire a whole department all at once. Somehow he got the university to keep these positions open. He didn’t feel like he had to fill them right away. I think he hired Boyd Pearson, Louis di Figueredo, and Sid Burrus in one year. Then I might have been in the second year or the third year of his development. Later, he hired Bob Jump the year after me in computer engineering. So, I think over maybe a five year plan he built up a whole pretty big department of people in signals and systems.

Nebeker:

That was fall of ’67 that you went to them?

Parks:

Yes. He really encouraged me to do teaching, and I met Sid then. Sid was my model teacher. I didn’t know how to teach. I don’t even think I had even been a TA. I had been a teaching assistant at Cornell part of the time. So I had some experience. Sid and I started talking to each other about different kinds of things. He had done some work on nonlinear systems at Stanford for his thesis. My first DSP student was my first student Ralph Warmack who got his master's degree in 1968. So, it must have been maybe within the first year. It might have been Ralph who asked me about digital filters.

### Digital signal processing

Nebeker:

Was that the first topic in digital signal processing you took up?

Parks:

Yes, digital filters. The digital signal processing didn’t really exist at that time. There wasn’t any course in it or anything. The Oppenheim and Schafer book hadn’t been written yet. But there was a lot of interest in the geophysical community. I’m trying to think if Ralph already worked for one of the geophysics companies. In fact the FFT was invented there, before Cooley’s paper.

Nebeker:

I know the oil companies, at least some, were using digital techniques in the ’50s.

Parks:

Yes. And I don’t know if Ralph Warmack was working for one of those companies, or had a summer job, or for some reason he was interested in recursive digital filters. I remember another influential person was Jim Kaiser. Ralph and I went over to a lecture at the University of Houston.

Nebeker:

Yes.

Parks:

But he gave a lecture on digital filters. But there was a paper that Ralph and I read several times on digital filters that Jim had written maybe in ’66.

Nebeker:

Yes, I know what paper you are referring to.

Parks:

It’s a famous paper. We studied it before we went over there and we listen to him and we went up and talked to him after his talk. So that was probably when I first started getting interested in digital filter design.

Nebeker:

I’m curious, why different people were getting interested in digital techniques and digital filters. Why was it interesting to you? Or to Ralph Warmack?

Parks:

Well, because you could do things on a computer. Practically speaking, I had so much trouble building this match filter for my masters thesis, winding these coils and all of this stray capacitance. It’s not easy to build these analog filters and I thought, “Gee, this is really easy. I can just write a computer program, and it will always do the same thing every time. I don’t have to keep tuning the coils and it’s great.” And it was new and different.

Nebeker:

Now I know that Ben Gold said that, in the beginning, they thought of the digital filters as a means of simulating a filter which then would be used on that analog.

Parks:

Yes, exactly.

Nebeker:

Were you at this point thinking of this as something that might just be simulated on a computer, or actually carried out in digital filtering?

Parks:

In fact, you've reminded me of something I forgot about. That is really where I first started digital signal processing, at Cornell Lab. They did a lot of simulation work. They tried to simulate different kinds of aircraft. In fact they were known for having a plane that would fly like a lot of different kinds of aircraft by having control system that simulated other aircraft. They did a lot of digital simulation. There was another report that you ought to find, the report on Project SAFE or the Schultz and Frier Effort. It was written by Bill Frier and I forgot what Schultz's first name was. But it was written at Cornell Lab and it had to do with simulation of analog filters on a digital computer. They invented the bilinear transform which was a popular way to simulate analog filters onto a digital computer. So, I was interested in the simulation part of it then. And also at GE we were simulating analog systems on the digital computer with FORTRAN and card decks. I started doing simulation initially, but when I worked with Ralph Warmack I think we were more interested in actually doing the processing with a digital processor that was a digital filter. And Kaiser’s paper, talked about the bilinear transform. I hope you talk to Ken Stieglitz too.

Nebeker:

I haven’t yet.

Parks:

He’s another very important person in the history of signal processing and the bilinear transform. He wrote his thesis on it. I thought his thesis was really great because it tied together this signal representation signal theory with the bilinear transform.

Nebeker:

Oh right. I remember his thesis was something like relating analog filter theory to digital.

Parks:

Yes. And Kaiser’s talk at the University of Houston was about the bilinear transform. That does seem like an interesting way to design digital filters. But it’s not exact. You don’t just plug this in to the analog filter and the digital filter does what the analog filter does. And then Stieglitz showed, and I only appreciated his thesis later, that it is exact if the discrete data you have is Legere function coordinates not time samples. I think I may have oversimplified his thesis, but I thought that was really neat that if you do the bilinear transform of a continuous time system, you put the substitution in for S, and you get a discrete time system. But you don’t put time samples in you put Legere coordinates. Then it all works exactly, with no error. It’s perfect. I don’t know if too many people appreciate that, and I suspect it is going to come back and be used some day, because analog VLSI is coming back. We have been trying to hire some people. We hired one at Carver Mead. At Cornell and I think there will be big developments in analog VLSI as well as digital. I wouldn’t be surprised if there are analog filter banks some day that are lower power than the digital ones and faster. So Kaiser’s lecture at the University of Houston was very influential.

Nebeker:

I remember he did say he talked at a lot of places.

### Teaching digital signal processing

Parks:

Yes, he does. And it was a good idea. Then Sid got involved. He was getting interested in digital filters at about the same time, so we thought that we should start teaching it. That was really a great experience for me to teach DSP and we taught it together. We talked about the best way to teach it.

Nebeker:

When did you start teaching that DSP course?

Parks:

It’s either ’69 or ’70 at the latest.We wish now that we had written our notes, and it might have been Oppenheim and Schafer. Not that it would have been as good as that, but it would have been as timely as that. We developed quite a nice set of notes in teaching the course those first few years. The oil companies I think were interested.

Nebeker:

Ralph Warmack was a master's student?

Parks:

Yes, he got his master's degree and then he went to work for Amoco.

Nebeker:

It was some kind of geophysical signal analysis?

Parks:

It was just digital filter design, design of recursive digital filters using the bilinear transform.

Nebeker:

Well, I can imagine, I know that the oil companies were using digital techniques, at that time.

Parks:

Yes, that is a very likely reason that he wanted to do that. He didn’t go on for a Ph.D.

### Digital filter design research

Nebeker:

So when you were teaching this course, you thought that this was an emerging area? That it would become much more important?

Parks:

I don’t know. Today’s assistant professors are much more savvy, much more aware of what is going on. We were just having a good time.

Nebeker:

It was just an interesting subject for you.

Parks:

Yes, it was just interesting. We understood it and we could do it. We didn’t have a research plan, or we didn’t say that this is a great career for us or anything. It was just something that we liked doing. In fact, Boyd Pearson was another person that I think got me and Sid both doing research. He was one of the people that was hired by Henry Bourne at about that same time. Sid and I weren’t worried about careers or signal processing as a good career or anything, until Boyd woke us up. Then Sid and I wrote a joint paper. That was the beginning of my research.

Nebeker:

The time of the design of digital filters?

Parks:

Yes.

Nebeker:

1970.

Parks:

That was the beginning of my interest in research.

Nebeker:

That was an influential paper.

Parks:

Yes.

Nebeker:

It was included in that reprint volume that was very important.

Parks:

But, personally, it got us interested in research. We were just playing around. I mean, we like digital filters, and difference equations were interesting.

Nebeker:

Or some particular application for digital filters that you thought was really going to be big?

Parks:

No. Some of our new assistant professors are coming in and saying, “Yes, I know wireless is a big area, and I want to teach wireless and I’m going to get in there. I know I can get funding from these agencies.” And they've got their careers all planned. We didn’t.

### Arden House Conferences

Parks:

And then the Arden House Conferences were the next big influence after that.

Nebeker:

Did you go to the ’70s one? The first one was ’68.

Parks:

No, we didn’t go to the first one I know that. They were every two years I think?

Nebeker:

Right.

Parks:

I went up there partly because I wanted to go back home and see my mother and father, and some of my friends in Buffalo. It was a good excuse to go up there.

Nebeker:

What did you think of the Arden House atmosphere?

Parks:

Oh, I wish that we could duplicate that again. I mean, it was just the best conference I have ever been to. I don’t know whether that is a sign of age. There was something like a hundred people. They were all very open. I think they had Ben Gold, Larry Rabiner was there and Charlie Rader.

Nebeker:

Jim Kaiser was there?.

Parks:

Jim Kaiser was there, and all of the people that Sid and I had heard about were there, at this conference. They were very friendly, and didn’t seem to be keeping secrets or anything. They just shared all their new ideas and everything that they were working on. I think that everybody had the same attitude. Everybody heard every talk, which lead to a lot of interesting discussions because we all had a common background. And you could walk around outside in the grounds and talk. I got to know Ben Gold there. Ben always liked to walk a lot.

Nebeker:

That reinforced your interest in the field?

Parks:

Oh, yes. The idea of doing research didn’t really occur to me, until I was kind of awakened by Boyd Pearson that I’d better publish. Then once I published then people read the paper and thought it was interesting. That kind of gives you a positive feedback, and you think, “Hey, maybe I can do this stuff after all.” So, you get to like it, and it was fun talking to people at Arden House.

### Parks-McClellan algorithm

Parks:

I’m almost up to the Parks-McClellan algorithm here.

Nebeker:

Yes, that was published in ’72.

Parks:

There was a Princeton conference that goes on, every other year. It’s at Johns Hopkins on alternate years. I don’t know the exact name of it, but it's in March. I don’t know whether that was the same year as the Arden House in ’70 or ’71. But that is where the Parks-McClellan algorithm was invented by Parks and McClellan actually. Schuessler wrote a paper on design of equiripple filters. He and Otto Herrmann wrote down the conditions for an equiripple filter and how many ripples there had to be. They had a pretty straightforward way to solve the equation, to get the coefficients for these equiripple digital filters. Ed Hofstedter gave a talk at the Princeton conference on a faster way to solve Schuessler's equations. It was an exchange algorithm. The problem with Schuessler's equations was that they were written down so that you made sure the error was the same. It was equal height ripples. But you didn’t know where the ripples would occur. You didn’t know which frequency would have the peak values. So what Ed Hofstedter did is he started with some initial frequencies and then iterated the frequencies and tried to find the frequencies where the peaks were in the error. During his talk, I thought that sounded like the Remez exchange algorithm. Jim Thorpe had taught a course at Cornell on Approximation Theory. I think it was EE5670. So I had learned about the Remez exchange algorithm from Thorpe and I continued to thank him for teaching me that because it looked like Ed Hofstedter was doing the Remez exchange algorithm. Except it was slightly different because Ed was solving Schuessler's equations which were the constant height errors. The Remez exchange allows the error to get bigger on every iteration. So I went up afterwards and asked Ed, “Isn’t that the same as the Remez exchange algorithm? Is that what you are doing?” And he said, “Well, maybe it is.” I think that he knew about the Remez exchange algorithm and I said, “Well, why don’t you just solve the problem directly using the Remez exchange?” And he said, “Well, I don’t know. It’s not what Schuessler wrote down. Schuessler wrote down these other equations, and I was finding a fast way to solve Schuessler's equations.” Which he did. I think Al Oppenheim was working on the problem too at the same time. I think that Al might have written a conference paper on equiripple filter design. I think Ed Hofstedter was at Lincoln, MIT Lincoln Lab. I believe that Al might have been working with him. Anyway, Ed said, “Yes, it probably is the Remez exchange algorithm.” So I went back and he said, “Might be a good thing to work on.”

Parks:

I told Jim that I thought the Remez exchange was interesting, Remez exchange and everything. Jim McClellan was working at Boeing had a lot of experience writing computer programs. He had worked for Boeing in Houston. His father worked for Boeing and the family moved around. Fortunately for me, Rice was convenient for him and he went to Rice. So he started thinking about writing programs to do this Remez exchange algorithm. We started counting ripples very carefully and discovered that Schuessler had one more than he had to have. It wasn’t necessary to have this many ripples or extremals. That made the whole algorithm easier to understand. It really was just Remez exchange algorithm. And fortunately nobody else had done that yet. Jim wrote the program pretty quickly and it worked, and then we gave it to everybody. And because Al for example was working on it, he appreciated it. You know other people had been working on the problem and so, “Hey, this is great. This works and we will try it and we will design filters this way.” People liked it and used it.

I think Al Oppenheim was the first person that called it the Parks- McClellan algorithm. It was the first place that I ever saw it written down, anyway. He referred to it as the Parks and McClellan algorithm. So I was really lucky that Jim was an eager, focused person. He works on a problem until he solves it. Then it was reprinted in the IEEE press program collection and things like that.

Nebeker:

I know that it was tremendously influential.

Parks:

Yes, I think it was very exciting for both of us to have people call and say, “Gee, I’m sorry, your program doesn’t work. I tried this and it doesn’t work.” Half the time it was typing mistakes because we just published the code, and they had to type it in back then. There was no web site where you could down load it. Some of the time there were interesting questions, that led to more research. People would come up and thank me for giving them the code. There was a guy from IBM who said, “You know we got this big contract because our filters were just that little bit better than other people's filters. All other things being equal, that is why we got the contract.”

Nebeker:

Jim Cooley was funny in talking about how because of the notoriety of the Cooley-Tukey paper, he has suddenly been regarded as this expert. And, he said that he got a tremendous education from trying to answer questions.

Parks:

Yes. The phone calls taught me a lot.

Nebeker:

And he is still working with you?

Parks:

Yes, for a Ph.D., and that was a lot harder because the whole idea of equiripple. The error changes sign and then comes back in positive, and everything got more complicated because you have a function in two variables, and then what direction does the ripple go? You have this idea of direction now that you didn’t have before. So, he invented the McClellan transform. He figured out how to design filters that were optimum 2D filters in some cases, based on a one D prototype. In those days people got Ph.D.'s in a shorter time, so he left after that. I wished he had stayed a little bit longer to discover what Mecklenbräuker discovered: that the McClellan transform could be used not only for design, but also for an efficient implementation of the 2D filter. If you designed you filter from the McClellan transform which is a mapping from one to two dimensional then you could actually implement that filter as a one dimensional filter, which is much more efficiently implemented than as a general 2-D filter.

Nebeker:

They are a little more expensive than digital filter.

Parks:

Yes, and I think analogs do better.

Nebeker:

Work fine, lower power. You will talk to an analog tape recorder?

Parks:

Oh yes. Digital is overdone. It’s signal processing that is interesting, and any way that you do it is fine, optically, digitally, analog.

### Sabbatical; research at Lincoln Lab and Schuessler's lab

Nebeker:

Okay, so you found yourself in the middle of the DSP community?

Parks:

Yes, all of a sudden. That was great. Then another great thing that happened was that I had a sabbatical coming up in ’73, and Schuessler invited me to Germany on the Humboldt program because he had been my master's thesis advisor. I went over there and on the way I spent the summer at Lincoln Lab, and worked for Ben Gold. My wife is from the Boston area. I do all of these things for the wrong reasons, not planning my career, but she grew up in Beverly, Massachusetts, near Boston. We thought that it would be fun to stop there during the summer.

It was great working for him, because I learned about number theory transforms. Charlie Rader was interested in them. Irving Reed, of the Reed-Solomon codes, was there visiting in the summer. Ben was always interested in fast transforms. He was the greatest person to work for. He was very casual, laid back and basically, you could work on anything that you wanted. I think that there were three of us in the office, Don Johnson, Dan Dudgeon and myself. Don helped me learn to write programs, on a computer across the hall that had a paper tape drive. But most of the interesting things were kind of what we called number theory transform.

Nebeker:

You were there for a whole year?

Parks:

Yes. I went the whole academic year. I supervised a student on number theory transforms. I think we did some reasonably good work, but Schuessler insisted on getting the program running on his PDP-11. Maybe he was right that it should have been implemented and running, but the students didn’t spend as much time on the theory as I thought they should. And Sid was starting to work on the theory transforms at about the same time.

Nebeker:

What was the state of the art in Europe at that time, of DSP?

Parks:

What, signal processing?

Nebeker:

Yes.

Parks:

Oh, that was interesting I think Schuessler's Lab was one of the most advanced labs in Germany. There was another one, I don’t know where it was, but Fettweis was the professor.

Nebeker:

Yes, at Aachen.

Parks:

He had a pretty big group doing digital filters. But in Germany, those were the two biggest places.

Nebeker:

Yes, I think that is right. I know Maurice Bellanger was at the Philips Lab.

Parks:

Yes, I think they were pretty advanced in digital stuff then in ’73. I had to turn down a Fulbright fellowship, at least turn down the money because I had this Humboldt that Schuessler had offered me and I couldn’t very well say, “Thank you, Professor Schuessler, but I don’t want it.” But the Fulbright people let me retain the title, even though I didn’t take the money. They put me on their list for being available to give lectures in Europe. There was a lot of DSP activity in 1973.

Nebeker:

So it was Vito Capellini.

Parks:

Yes, Capellini. I like to travel places with my family, and I went with my wife and two children to a conference in Florence. Capellini invited me to give a talk on this Fullbright when I was there. We drove down to Florence and he found this great place for us to stay and took us out to lunch. It was really a very charming evening.

So I enjoyed visiting different places in Europe. At the Imperial College they were doing some DSP. But I think that Schuessler's group was very advanced. They insisted on building hardware. I can remember that Fettweis and Schuessler argued with each other about the right approach to building a digital filter. I think Fettweis raved on digital filters and Schuessler didn’t really think that they were that good. They finally decided that “Well, we will write down some specs for a filter and you build yours, and I will build mine, and then we will compare them.” They wheeled these carts of equipment into this room. I don’t know how they finally decided or probably they didn’t either agree that one had actually triumphed over the other. They did a lot of construction of things. They really insisted on building things.

Nebeker:

Do you think that was valuable at this point?

Parks:

Yes I think that it was very valuable. I probably complained about Schuessler earlier. I wouldn’t have insisted that the student implement the number theory transform. I would have encouraged him to do some more theory and publish it. But I think that Schuessler was right in building digital filters and special purpose hardware and things like that. Jim Kaiser always said this too. I hope you have captured Kaiser's story about the oscillator somewhere. Have you asked him about his oscillator story?

Nebeker:

No.

Parks:

My translation of it is that he was designing a digital oscillator and so he calculated the coefficients so that the poles would be on the inner circle so it would oscillate. He had a technician build it. He was going to build in the lab, and check it out and make sure that it worked, and he came back to his desk and did some more calculations. And then he discovered suddenly that it wasn’t going to work because of quantization of the coefficients. You know, you overlook the quantization and you put the poles on the circable. When you quantize the coefficients, which you have to do when you build it, they fall on a grid and the grid didn’t allow them to be exactly on the inner circle. So it wasn’t going to oscillate. So we went back to the lab and was worried we were going to have to change it. Then we discovered that there it was oscillating with no problem. It turned out that it was in a limit cycle. So, he started to learn all about limit cycles, nonlinear effects, and digital filters. So, it was oscillating, but not because the poles were on the unit circle, but because it was in a limit cycle. So that is his story about how actually building the theory could lead to more research questions about limit cycles.

I’m at Kodak right now. I’m learning a lot by actually doing things. I mean actually processing real images and, so to speak, building things. There is no substitute for that.

### Publications and consulting work

Nebeker:

So you had a good year in Germany?

Parks:

Germany was great. Then I came back and Jim Cooley came to Rice and gave a talk. He said to me, “You might want to look at the National Academy. There is a paper in there that you might find interesting…” It was a paper on computational complexity of convolution and FFT algorithms, and Jim wasn’t really allowed to tell me much about it, because IBM wanted to keep it a secret but still wanted to publish it somehow. I tried to read it, and I couldn’t read it. So I had a really good student Dean Kolba who was interested in it, and so we spent the whole summer reading this paper. It was based on some of the number theory ideas that I had learned in working with Charlie Rader and Irving Reed, the year before. So over the summer Dean Kolba and I finally managed to understand what it was and we published a paper on it.

Harvey Silverman was working on the same DFT/FFT implementation at IBM. I was really flattered to get a call. Jim called me and said, “Would you mind holding up your publication a little bit to let Harvey’s paper come out first? Well, you know, Harvey had done a lot of work at IBM, and it really was an IBM idea originally, and I told you about it. I thought, “Gee, you really think my paper is that good? I will be glad to.” So we published just a month or so after Harvey’s came out. And it got an IEEE paper award. In fact I got a few phone calls about that, people thanking us for writing it so they could understand it.

Sid and I started writing some books in the ’80s. We started talking to TI. Then I got interested in consulting. I hadn’t done any. I was so frightened by Boyd Pearson that I wasn’t going to get tenure, that I figured I better publish papers and everything, and I didn’t have time to do any consulting. John Ingram who had been a Rice professor was working at Schlumberger in Houston and one day invited me to come over to Schlumberger and look around and see if there were any problems that I thought were interesting and I might want to work on as a consultant. I got interested in acoustic well logging or sonic well logging and the signal processing that’s associated with that. So I got into sonic signal processing and well logging and started doing some things there, in the early ’80s I think. That was fun, because it was real world signal processing and I got a patent or two for some algorithms that they still use I think.

Nebeker:

And it was the case there that this application spawned some new ideas?

Parks:

Yes, I think so. Jim McClellan actually worked for Schlumberger for awhile. He first went to Lincoln and then he went to MIT in the faculty and then he went to Schlumberger. He again came along and wrote up some of the code in better form. At Schlumberger, my boss, Frank Morris, and I developed some algorithms for estimating the speed of sound in rock. And they are still being used. There is a patent for what is called TKO now and the algorithms have been refined and improved. We wrote a paper with five or six authors. Jim was one of them. So, that is kind of something I look back on as useful. That was early ’80s I think. Those were the good years in the oil industry.

They would ask me to go to conferences. It was a new area, and new problems, something to work on. Every ten years they needed to work on something new I think. So, I worked on sonic signal processing. Sid and I started talking about working with TI at the same time. They were interested in writing some books. We wanted some books out there that say DSP and TI. So we thought that was a good idea and, as I said in the beginning, we were lazy. We sure wished we had written that first DSP textbook. I wrote some of the information on FFT and algorithms. We worked together a lot in the beginning on this number theory and convolution. I think Sid was away that summer. Yes, he was in Germany in fact. So we were in separate places working on the same thing without knowing it. So we got together and wrote the book.

Nebeker:

Now those two books were, I believe, quite influential because you provided all of the programs.

Parks:

Yes there were a lot of programs. In fact, that was TI. It is a great company as far as insisting on practical application. They wanted more and more code and Sid and I would resist putting programs in because they wanted TI specific code. Code that would work on their DSP processor and we usually put general things in the book. So we compromised. I think some of the programs were written by some TI employees with TI code. Then we wrote a filter design book after that, in the same series as TI series.

I would still like to go back to TI. I have gone down there and made videotapes. I made a videotape short course for them once. I wish I were at a Texas University because they pay more attention to me. I think that they are correct in thinking that it is harder to retain employees that come from the northeast. It is easier to be sure that you are going to keep people you hire that are already from Texas.

### Cornell employment, funding, and research

Parks:

When I first went to Cornell, I was kind of proud of being from Texas, so I thought I should have Texas Instruments equipment in my DSP lab. So, they not only donated the development systems for the TMS 320 DSP, but they also donated the PCs to go in them. They put the boards in and everything, so I started with a DSP teaching lab at Cornell when I went there.

Nebeker:

When did you go to Cornell?

Parks:

Nebeker:

What had been the principle areas that you have worked on since you went to Cornell?

Parks:

Well, I worked on time frequency analysis. That was something I had started working on at Rice, just before I left. Faye Boudreau was a Ph.D. student of mine at Rice. Then, I continued to working on that at Cornell, and had a very good student Ram Shenoy. He was the top of his class at Cambridge. He is still a very great contributor and mathematician. He did a lot of good work in his Ph.D. thesis on time frequency analysis, group theory, group representation theory. I have been working on things like that in addition to multi-rate systems ever since.

After Jim had done the one dimensional filter design for his master's thesis, I can remember talking to Larry Rabiner. Larry was very interested in the one D filter design results and ran a lot of examples in the code. He figured out how to use it better, and relationships among all of the parameters and everything at Bell Labs, and wrote some papers on it. So Jim and I had been talking to Larry, and I can remember asking him, “Well, what is the next thing? What should we work on now after this one D thing?” He said, “Multi-rate.” Jim and I couldn’t figure out what there was about multi-rate systems. They are the same number of multiplies, you just rearrange everything. So we never really got it. We didn’t work on multi-rate.

But, he was right. The multi-rate area has really grown rapidly, multi-rate systems. In fact, some people think that wave lifts are just multi-rate filter banks. I think the area of wave lifts is made up of multi-rate systems, multi-rate filter banks, signal theory, mathematical functional analysis and things like that. Multi-rate systems are very important. Larry and Ron Crochiere wrote that book on multi-rate signal processing. I think that book is still in print. It’s a good book. Now I’m working on multi-rate systems.

Nebeker:

You had a few other things to work on first.

Parks:

Yes, but I think that they are still useful. There is still some interesting problems in multi-rate systems and wave lifts and that connection. I just finished teaching a short course at Kodak since I was on sabbatical. They said, “You know why don’t you just teach us something while you are here?” So I taught multi-rate signal processing wave lifts to them. I learned some more things about application to images that are interesting. I want to work on that some more.

I had one other thing that changed when I went to Cornell, I needed more money, didn’t realize what a good deal I had at Rice. Rice didn’t charge tuition for graduate students, Cornell did. So I had to have two grants. I had to have a NSF and ONR. The ONR supported me for a long time. Fortunately, I had done the well logging work on transients and acoustic pulses and everything, which was related to some of the Navy interests. So I could get some Navy funding, to do that same kind of well logging work with a different name. So it kind of broadened the things that I worked on. I worked on different things because I had two different grants. I still worked on transients. Another thing that I started working on at Cornell and that I’m still interested in and my daughter got interested in is bioacoustics. There is a bioacoustics lab there and a lab of ornithology. They have a lot of recordings of bird songs. They hired Chris Clark who had studied whales and was interested in bioacoustical problems connected with studying whale migration, whale census studies and things like that. So, I did some work with that group on acoustic signal processing.

Nebeker:

That is really a striking thing about signal processing. That you can have these applications from all over.

Parks:

Yes. My daughter got interested in it. She is a biology major, she’ll be graduating from Cornell in a week. She had done some undergraduate research projects over at that bioacoustic lab, and now she is going to MIT in the joint program with Woods Hole [Oceanographic Institution].

Nebeker:

Very interesting career that you have had so far.

Parks:

Yes.

Nebeker:

Well, it sounds like you are involved in more things than ever.

### Sabbatical at Kodak

Parks:

Yes, I have awakened. I mean, it’s really good to go on sabbatical. I think that is the main message to people. I was the first person at Rice that went on sabbatical. I’m so glad that I went to Kodak on sabbatical, because I have learned a couple of new things and found some new directions. I’m excited about applying signal processing to images. Everything is going to be done digitally. Kodak knows that they have to hurry up before HP catches them. So, it’s almost like the early days of DSP. It’s kind of an exciting time, a lot of rapid changes. Everything is driven by applications and real problems. It’s like Kaiser says, “You have to try it out and see how it works and maybe get some new questions.” I think that is a good story that he tells about the oscillator. I hope it is a real story, and I didn’t make it up. I will ask him.

Nebeker:

We’ll check it out. Thank you for the interview.