“A Fixed-Point Recursive Digital Oscillator for Additive Synthesis of Audio”

Article by Todd Hodes, John Hauser, John Wawrzynek, Adrian Freed, and David Wessel, published in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99, March 15–19, 1999), pp. 993–996.
4 pages.

Abstract: This paper summarizes our work adapting a recursive digital resonator for use on sixteen-bit fixed-point hardware. Our modified oscillator is a two-pole filter that maintains frequency precision at a cost of two additional operations per filter sample. The new filter’s error properties are expressly matched to use in the range of frequencies relevant to additive synthesis of digital audio and sinusoidal modelling of speech in order to minimize the additional computational overhead. We present the algorithm, an error analysis, a performance analysis, and measurements of an implementation on a fixed-point vector microprocessor system.

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Adobe PDF document, 1999_Hodes_DigitalOscillator.pdf.

Other versions

For reasons unknown to me, this article was republished in almost identical form by Hodes and Freed—listing only themselves as authors—with the title “Second-Order Recursive Oscillators for Musical Additive Synthesis Applications on SIMD and VLIW Processors”. This second version can be found in the proceedings of the International Computer Music Conference held in Beijing, China, in 1999. Although I was among the authors cut from the second version, it was me, in fact, who adapted the oscillator algorithm to 16-bit fixed-point, the main topic of the article. (For the record, Todd Hodes implemented the algorithm in software and wrote most of the text of the article, including providing his own spin on the error analysis.) Since Adrian Freed nevertheless seems to take some pride in having improved his standing as author in the second version, I congratulate him for this accomplishment. Todd Hodes has graciously reinstated Prof. Wawrzynek and me as authors in the electronic copy of the Beijing conference paper available from his Web site—thus creating a third version with yet a different author list, not matching either of the published ones.