The Synthesis of Complex Audio Spectra by Means of Discrete Summation Formulas Journal of the Audio Engineering Society, Volume 24, Number 9, November 1976, pp717-727. "A new family of economical and versatile synthesis techniques has been discovered, which provide a means of controlling the spectra of audio signals, that has capabilities and control similar to those of Chowning's frequency modulation technique. The advantages of the current methods over frequency modulation synthesis are that the signal can be exactly limited to a specified number of partials, and that 'one-sided' spectra can be conveniently synthesized." That was the abstract of the paper.

Linear-Phase Bandsplitting: Theory and Applications (with Mark Berger) Presented at the 76th Convention of the Audio Engineering Society, October 8-11, 1984, New York, Preprint 2132 (session A-1) "There are a number of applications for banks of bandpass filters in professional audio studios, both for film and music production. In this paper, we explore digital techniques for bandsplitting that have the property that the spectrum may be separated into a number of bands such that when these bands are added back together, the result is a pure delay. There need be no amplitude or phase distortion other than delay. This allows such applications as linear-phase graphic equalizers, multi-band noise gates, and many other improvements over conventional studio equipment. These algorithms have been implemented on a large-scale audio signal processor and run in real time. They are currently being used in major motion picture production."

This is probably my most-misunderstood paper. Most people pick up on the noise-gate stuff, which led to the NoNOISE work I did at Sonic Solutions (after many refinements, most of which are still proprietary so that I can't disclose them). What I consider the most important part of the paper is that the effect of certain families of window functions such as Hamming, Hanning, Blackman, or any that are finite sums of harmonic sinusoids can be calculated in closed form. I find this a remarkable result (although obvious in hindsite). If I want to divide the spectrum into 5, 10, 50, or 500 bands, I can compute linear-phase FIR impulse responses that will do that by evaluating formula (17). Note that the bands do not have to be equal-width. For instance, I could do something like a wavelet transform by having consecutive filters use wider and wider bandwidths. These will all sum to an impulse (by construction), so that they are guaranteed to be an identity. I know now that it is not limited to those window functions - that this can be done using any window function. That is, you can just write down the coefficients of the impulse responses of a set of filters that will divide the spectrum up any way you want. Maybe I should rewrite this paper sometime. Or maybe not.

The Use of the Phase Vocoder in Computer Music Applications Journal of the Audio Engineering Society, Volume 26, Number 1/2, January/February 1978, pp42-45. This paper is one of the first (maybe the absolute first) to show how to use short-term Fourier transform as a method of analyzing and synthesizing musical sound, but with the signal-processing rigor necessary to make the system an identity in the absence of modification. Probably the most ignored contribution, and the one I consider probably the most important, is the technique for unwrapping the time-variant phase. Equation (9) represents a largely foolproof unwrapping method that involves no heuristics. This paper led to much of the subsequent work by Dolson and others who have extended and refined the method for time and frequency modification of high-quality musical sound.

Signal Processing Aspects of Computer Music: A Survey Proceedings of the IEEE, Volume 65, Number 8, August 1977, pp1108-1137. This was an invited paper. Larry Rabiner invited me to write and submit this paper. It still stands as a reasonable survey of signal processing in music. It is interesting that synthesis is so little used today, whereas recording and playback (i.e., sampling) is so common. I guess it's a lot easier. Missing from this paper is any discussion of processing of the signal (aside from analysis). The computation for any interesting processing, except maybe reverberation, was so expensive at that time that we were not able to do much of it.

About This Reverberation Business Computer Music Journal, Volume 3, Number 2, June 1979. This is a somewhat rambling random walk through some investigations into room reverberation. I had originally submitted it to the Journal of the Acoustical Society of America (JASA). I got a scathing review back that I swear was longer than the paper. The reviewer complained that it was in "an antequated discursive style." Yeah, that's probably correct. The reviewer differed with me on several technical points. I thought about it a while and concluded that the reviewer missed the point and didn't know what he was talking about, and in at least one area was flat wrong. Rather than try to fight with the reviewer, I sent it to CMJ, who was quite happy to publish it the way I wrote it.

I should mention that I believe I got mixed up between feet and meters in the graphs of air attenuation with distance. You may want to check this in a real acoustics textbook if it is important to you.