Julius O. Smith III works on applications of digital signal processing to music and audio. Stanford identifies him as a professor emeritus of music and, by courtesy, electrical engineering, based at its Center for Computer Research in Music and Acoustics. His doctorate in electrical engineering was completed at Stanford in 1983.[ref]
His Spectral Audio Signal Processing by Julius O. Smith III explains how to extract a spectral envelope rather than treating every narrow harmonic peak as part of the slowly varying sound shape. One method uses a cepstrum: transform a logarithmic magnitude spectrum, retain an appropriate low-quefrency region, and transform back. This separates broad spectral shape from more rapidly oscillating harmonic detail under suitable assumptions.[ref]
Spectral Audio Signal Processing by Julius O. Smith III. Spectral Envelope Extraction, Cepstral Windowing and equations 11.2–11.3
For example, two played notes can have different harmonic spacings while sharing a similar broad envelope associated with the instrument's resonances. Distinguishing spacing from envelope helps explain why changing a note's pitch and changing its timbre are different signal-processing tasks. The separation is approximate: window choice and closely spaced spectral features affect what the method preserves.
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