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In the fall of 1998, Yonina Eldar, PhD ‘02, was a 25-year-old graduate student in MIT’s Research Lab for Electronics, meeting with her advisor, Alan Oppenheim ‘59, SM ‘61, ScD ‘64, for an initial discussion of her dissertation topic. Eldar had studied physics as an undergrad, but in the intervening three years she’d earned a master’s in signal processing, joined a startup commercializing wireless technology, and become a mother. “I was very remote from physics when I came to talk to him,” says Eldar, now a professor of electrical engineering at the Technion in Israel and a visiting professor at Stanford.

Eldar expected that Oppenheim, who has led MIT’s Digital Signal Processing Group since the mid-1960s, would follow the practice of most thesis advisors and present her with some of the unsolved problems in his field before sending her home to read papers that would help her zero in on one of them. But that’s not what happened.

“He right away said to me, ‘So, I think it would be nice to use quantum mechanics in signal processing,’” she says. “And I just kind of stared at him. After I kind of got a grip, I said, ‘Sure, that could be interesting. What did you have in mind?’ And he looked at me and said, ‘I have absolutely no idea. Why don’t you go find out?’”

It’s a commonplace that innovative ideas often result from unorthodox thinking, but few scientists try to cultivate unorthodoxy with the zeal that Oppenheim does. Eldar’s experience is not atypical: Kevin Cuomo, for instance, a 1993 graduate of Oppenheim’s group, wrote a thesis inspired by chaos theory, a branch of mathematics more typically associated with weather systems than with signal processing; Tom Baran, a current grad student, is tracing out analogies between signal processing and thermodynamics. Other students have found implications for signal processing in fractal geometry and the physics of solitons (wave crests that keep their shape while traveling long distances at a fixed velocity). But while the dissertations of Oppenheim’s students may be speculative in their origins, they’re very concrete in their results: so far, they’ve led to the filing of 19 patents, including one for Cuomo’s work and four for Eldar’s.

The most intuitive examples of signal processing involve communications signals, such as phone calls, radio transmissions, or videos streaming over the Internet. “Processing” might mean filtering noise out of a call, separating the voice of a DJ from the electromagnetic wave that encodes it, or compressing video data so that it takes up less bandwidth. But many other types of information can be thought of as signals, too. The Dow Jones industrial average, for instance, is a signal that carries information about the U.S. economy; the Wall Street Journal’s 30-day moving Dow average is a kind of signal processor, filtering out some of the noise of day-to-day fluctuations. A digital image, too, could be thought of as a signal: the color and brightness of successive pixels are like the successive frequencies of a radio transmission, and signal-processing techniques can sharpen an image or help identify the objects it contains.

The sheer variety of signals, and of ways to process them, gives Oppenheim confidence that no matter how far afield his students’ intellectual explorations lead them, they will eventually find their way back to some practical problem. So he pushes them to range farther. “Being a little scared is good,” he says. “If you don’t work at the edge of your comfort zone, your comfort zone will shrink.”

Eldar acknowledges that the open-­endedness of the questions Oppenheim poses to his students “could be discouraging.” But “you know that he’s done this a million times before,” she says, so “it’s actually motivating, even though you really have no idea what you’re looking for.” Baran agrees. “It’s not like anyone is really seriously worried about whether they’re going to have a thesis or not,” he says. “Al has an amazing ability to see how a lot of these ideas get integrated together.”

The birth of digital signal processing

The first offbeat thesis that Oppenheim steered to completion was his own. Today, most signal processing is performed on the fly by computer chips, but that wasn’t true when Oppenheim was a grad student in the early 1960s. At the time, electrical engineers would test new signal-processing algorithms on computers, but the algorithms could take hours or even days to execute. Once an algorithm had proved itself in simulations, it had to be wired into an analog circuit before it could be used.

But the young Oppenheim was convinced that computer technology would improve to the point that it could keep pace with real-time signals. “Looking back, I can’t decide whether it was the naïveté of a kid who thinks that if he keeps flapping his arms, eventually he’ll fly,” Oppenheim says. “But I had no doubt that someday the technology was going to make it possible.”

For his thesis, Oppenheim described an approach to signal processing that was totally impractical with analog circuits. After graduating, he joined the MIT faculty, but he soon took a leave of absence to do signal-processing simulations at Lincoln Lab. The large computers that ran those simulations were effectively digital signal processors; they were just doing the processing very slowly, on stored data rather than live signals. When Oppenheim returned to teaching, he offered the Institute’s first course on digital signal processing, and the following spring, with the help of Bell Labs’ Ronald Schafer, he began organizing his notes into the field’s first textbook, which was published in 1975 and is still widely used today.

In describing his group’s research style, Oppenheim is fond of metaphor. “Do you know how smart a bowling ball is?” he likes to ask. A bowling ball placed at the top of a hill, he explains, will find the lowest-energy path to the bottom, but to calculate the same path, a human would have to solve a complicated set of differential equations. Nature, Oppenheim believes, can suggest highly efficient ways of solving complicated problems, and looking to nature for inspiration is one of the themes that unify his group’s diverse research.

Eldar’s dissertation is a case in point. Extremely small particles—the purview of quantum physics—can be described by a host of properties. Some can be understood intuitively, like position and energy; others are more esoteric, like spin and “color charge.” But one of the central tenets of quantum physics—Heisenberg’s uncertainty principle—holds that measuring any one of those properties makes one of the others unknowable. Acquiring information about one property destroys information about another.

Oppenheim and Eldar saw an analogy in the case of a signal so corrupted by noise that recovering all the information it originally contained is impossible. Quantum physics provided them with a new way to think about performing measurements on the signal, in order to extract information of high value.

Another of Oppenheim’s slogans is that one plus one can equal three: that is, the best solution to a problem may be not just counterintuitive but seemingly idiotic. In some academic environments, Oppenheim says, proposing an offbeat idea will spark immediate derision. “I don’t do well in that kind of atmosphere,” he says. “I clam up, and I lose the ability to think on my feet.” But in other environments, he says, if you unthinkingly blurt out that one and one are three, your colleagues will help you make sense of the proposition in a way that ultimately brings a fresh perspective to a stale problem. That’s the type of environment, Oppenheim says, that he tries to foster in his group’s meetings.

“At the weekly group meetings, there’s no agenda,” says Cuomo, who after 20 years at MIT Lincoln Lab is now an engineer at Photonic Systems in Billerica, Massachusetts. “You just go in, and whatever’s on anyone’s mind, you discuss. It feels like a team effort in a way that other research groups don’t.” Adds Baran, “You learn very quickly that no idea is a bad idea.”

Teacher’s teacher

Not everyone has the luxury to adopt Oppenheim’s freewheeling approach, notes Jim Preisig, a scientist at the Woods Hole Oceanographic Institution who graduated from Oppenheim’s group in 1992. “He would have grants that gave him a lot of leeway in exactly what problems we were solving,” Preisig says. “And it takes someone of his stature to be able to do that.” But for Eldar, that’s all the more reason to value having studied with Oppenheim. “Once you’re into your career path and you’re trying to build a lab, build a group, you can’t just sit there for three years and say, ‘Hey, I’m going to see how string theory applies to this problem,’” she says. “So having those years is, I think, something really precious.”

Whether she knows it or not, Eldar is echoing advice that Oppenheim received from his own thesis advisor, Amar Bose ‘51, SM ‘52, ScD ‘56, founder of the Bose Corporation and an MIT professor for more than 40 years. Oppenheim says that when he was writing his PhD thesis, he had trouble interesting faculty in his seemingly impractical approach to signal processing. He was considering abandoning the project. Bose had agreed to advise Oppenheim because of their personal rapport, though the dissertation topic was somewhat outside his area of expertise. “He said, ‘Are you excited about it? Do you believe in it?’” Oppenheim recalls. “Then he said, ‘This is probably the last time in your life that you’ll get to pursue a question just because it’s interesting. If you believe in it, you should do it.’”

Another thing that Oppenheim says he learned from Bose was to appreciate how far his influence as a teacher could reach. “The wonderful thing about teaching is that you impact a generation, they go off and become teachers and impact a generation, and so on,” he says.

In 1988, Oppenheim won the IEEE’s highest educational award, which was presented at a ceremony presided over by James ­Kaiser, SM ‘54, ScD ‘59, and attended by more than a thousand people. Before introducing Oppenheim, Kaiser asked how many members of the audience had been students in his research group. About a dozen people stood. Then Kaiser asked who had been advised by one of Oppenheim’s students. A larger group got to their feet. Then Kaiser asked anyone who had taken one of Oppenheim’s classes to stand, then one of his students’ classes, then anyone who had read ­Oppenheim’s book. By the end, almost everyone in the room was standing.

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Credits: Christopher Churchill

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