Gary Nelson

The truth is I can't recall when Glen Culler entered my life at UCSB, but it was after finishing my Masters in '67. So it was after beginning the PhD program and must have been related to a Graduate Traineeship from NSF that I was lucky enough to obtain. At some fuzzy point in the past I simply recall Glen being there at a board explaining his views on a wide variety of topics.

One memorable project was the "mercury keyboard." Others have mentioned Glen's desire to build a better keyboard. "Wouldn't it be nice if we could use mercury to make a keyboard," he mused one day. A flexible membrane, a reservoir of mercury, squeeze the mercury up a small tube to short together X and Y conductors -- wallah!! A keyboard!!

I got the task of building a prototype. Jeezus! What do I know about making such a thing? Absolutely nothing. That seemed to qualify me as having no preconceived ideas so I was off. After about 200 calls to various plastics vendors I found a source of silicon rubber sheets and an epoxy resin that would make a molecular bond to said silicon rubber. The box arrived from the vendor, and equipped with a few strips of thin stainless steel for the conductors, I made about the crudest looking prototype imaginable on my dining room table. Not knowing any better I made a mold of modeling clay and cured the resin in my oven. After a few unsuccessful globs, I began to get ugly but functional units.

Today, of course, I have an appreciation of the toxicity of Mercury, but in those days it was fun stuff and I loaded the switches with the silvery liquid in my kitchen. Finally, I assembled my best of breed example of the "Mercury Keyboard Prototype" and took it to Glen. With the switch hooked up to a scope, Glen pushed the button, the contacts successfully closed and history was made as Glen said something like, "Well that doesn't work." He was right of course.

At some point, Glen got a grant from some government agency to investigate speech analysis. I recall working with Gordon Buck, Dennis, and Ray to lash a large (7 inch or so) Tektronix storage onto the IBM 1800 minicomputer. The 1800 had A/D and D/A channels, so we could capture a single word of speech (was it 16 kB of RAM?) and play it back. We had obtained a couple adjustable audio filters and were looking at the speech waveforms after different amounts of bandpass filtering.

One day several of us were huddled around Glen with a microphone, speaker, filters, and the display. I was standing behind Glen looking over his shoulder at the squiggles on the screen when he said emphatically, "Damn, those look like Hermite Functions!"

Hermite functions!? What the hell are Hermite functions I asked myself. I don't recall who else was there but we looked at each other and all realized that we had no idea what Glen was seeing. Finally one of us asked, and Glen explained that Hermite functions are solutions to Schroedinger's wave equation from Quantum Mechanics. From that moment onward, we were on the track of the "fundamental particles" of speech analysis.

Each such wavefunction could be characterized with five parameters, the ASCON parameters for Amplitude, Spread, Center_time, O was phase from phi, and N was the wave number. I don't recall now when a "simplification" entered the scene, but for N larger than maybe 2, the "true" wavefunction was closely approximated by a Gaussian envelope modulating a sinusoid and a new analysis tool was born--ASCOF analysis where the F is Frequency.

I spent a lot of time trying to understand what was "going on" with these wave functions for speech analysis and found a paper in the UCSB library by the Nobel laureate Dennis Gabor written in the 1930's describing basically the ASCOF approach, but done at a time when no tools for analysis existed. Then I found an obscure paper by Yilmaz that *derived* these same functions from a completely different approach based on information theory. Despite these strong indicators of fundamental underpinnings, none of us were able to develop a formal mathematical structure for the tools. Instead, we all developed heuristic tools for decomposing a speech wave into its constituent wavefunctions. While the ASCOF approach was "interesting," and could analyze and then reconstruct a waveform with greater precision than other existing methods, the lack of formalism was (in my opinion) a deterrent to wider acceptance of the approach. UCSB was the only place the work was done. Another issue was that as a means to compress speech bandwidth, ASCOF was not at all outstanding.

Glen was convinced that these were the fundamental building blocks of speech analysis and left UCSB to form Culler-Harrison to apply the techniques. Linear Predictive Coding emerged, was excellent at bandwidth compression, and became the bandwagon to be on. ASCOF analysis dissolved into the mists. In the last few years, however, Glen's original intuitions about the more fundamental nature of these tools has been verified. Other researchers have independently rediscovered these functions and they have become a hot topic called WAVELETS. I have perused a couple books on the topic of Wavelets and none of the Culler/UCSB work is referenced as seminal contributions. Gabor's work is recognized, however. Only those of us who were working with Glen in those early ASCON/ASCOF days recall that it was actually Glen Culler who "discovered" those functions buried in speech.

One of the most important lessons I learned from Glen was that, if our path continually gets more complex and baroque instead of more elegant and simple, we should always have the courage to throw away our work and start over. Good advice that I have always strived to heed.

Finally, I want to say that the Culler-Fried OLS was a wondrous tool for mathematical problem solving. It positively spoiled me. Once I saw how easy it *could be* to analyze a problem using the OLS, using FORTRAN was, well, nauseating. It has been over 25 years and the best we have today is spreadsheets, Math Cad or Mathematica and these are not easier to use than the OLS. If the OLS had enjoyed 25 years of improvements, the user interface to computers would be far better today methinks. I continue to be amazed at the way the "market" selects "winning" technologies. I guess we needed a better PR department.

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