Harker Aquila spoke to Dr. Ronald Schafer, an adjunct professor of electrical engineering at Stanford University notable for some of the earliest research in digital signal processing (DSP) and contributions to speech processing, about his work and the history of the field.

Dr. Schafer, who is the father of biology teacher Dr. Kate Schafer, guest lectured to math teacher Dr. Anuradha Aiyer’s fifth period Signals and Systems advanced topics class on Nov. 15. He has coauthored multiple influential textbooks, including “Digital Signal Processing” and “Discrete-Time Signal Processing” with Dr. Alan Oppenheim, his doctoral adviser and an author of the textbook used by Dr. Aiyer’s class.

The text of the interview with Dr. Schafer, which has been edited for style and length, follows.

Harker Aquila: Could you give me some background on your academic career and what you’re currently teaching at Stanford?

Ronald Schafer: The Stanford course is EE264. It’s called Digital Signal Processing. That course generally runs in the winter quarter. In that course, we’re actually working with a young man from Apple Computers who has an interest in teaching, and we’re putting a lab experience with the course where the students are implementing real-time digital signal processing functions on special DSP chips, and also this term, we’re using the processor in iPhones and Android phones as a processor to implement DSP functions. We’ll see how that goes; it should be interesting for the students to be able to put a DSP application on their iPhone.

HA: What would you want students to take away from the presentation?

RS: I would like them to take away the notion that understanding the mathematical basis for representing signals and systems is important, that it’s a strong basis for understanding how machine learning these days can be applied to solve lots of interesting problems. I think it’s important to understand the signal and to do that in terms of the mathematical theories that represent signals and not just treat the machine learning algorithms as a black box that you throw it enough data and out comes the answer—but I’ve been doing digital signal processing for 50 years, and I probably think it’s more important than other people do. You asked my history; I received a Ph.D. with Dr. Oppenheim back in 1968, a long time ago, and then I worked at Bell Laboratories for about seven years. Then I was at Georgia Tech [the Georgia Institute of Technology] for 30 years; then I moved out here and worked at Hewlett-Packard Laboratories for eight years, and now I’m totally retired except for occasional courses that I teach at Stanford.

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I think it’s important to understand the signal and to do that in terms of the mathematical theories that represent signals and not just treat the machine learning algorithms as a black box that you throw it enough data and out comes the answer.

— Dr. Ronald Schafer, adjunct professor of electrical engineering at Stanford University

HA: How did you decide you wanted to go into engineering and DSP?

RS: Well, I don’t know. I was interested in science, but I was also interested in practical things, and I started out going to a small liberal arts college, and there was a professor there that I sort of resonated with. He was an old guy at that time. He taught many years at the Naval Academy, and he couldn’t retire, so he got a job at this small school called Doane College [in Crete, Nebraska.] I just got interested in science and math, and I finally decided that what I wanted to do was apply those things to solving problems, so I took an engineering degree at the University of Nebraska. Then I decided I wanted to teach electrical engineering, and so my father-in-law, who was a professor there, told me that I should get a Ph.D. from the best school that would accept me. MIT accepted me, and I went there and did a Ph.D. I was very lucky because DSP was just starting when I was looking for a thesis, and so I was able to do some things that hadn’t been done before, but it was simply because of a convergence of things like the FFT [fast Fourier transform] and the ideas of digital signal processing that were being developed. I didn’t set out to study DSP, but I did. It’s like many things that happen to us in life. You take opportunities when they arise, so I benefited greatly from taking an opportunity that came up.

HA: What do you think the most important factors in developing DSP have been?

RS: The basis or the beginning of digital signal processing occurred at basically MIT Lincoln Laboratory and Bell Telephone Laboratories, and people began to see that it was important to do digital representations of signals because of the advantages of those representations and that eventually, there would be computational power enough to implement things like filters, and in 1965 a paper was published describing what is now known as the FFT, and that triggered off a huge number of pieces of research. People began to see that instead of using the Fourier transform as just a mathematical representation, it could actually be used in computation. I think that 1965 was a watershed year in the development of digital signal processing. Then, in the early ’80s, about the same time that PCs were becoming feasible and widely sold, people at places like Texas Instruments began to make special-purpose digital signal processing chips that were designed to implement the DSP algorithms—the filters, FFTs and so on—and then developments in integrated circuits have just mushroomed to the point where computational power is gigantic, and memory capability is gigantic, and so forth. All of that now leads to these ideas of machine learning, where you basically learn a nonlinear digital signal processing system whose purpose is to take signals and produce information from them, so it’s been a very exciting time over the past 50 years or so. Lots has happened. There’s lots left to be done: things for you to do, if you decide you want to go into engineering or computer science.