= Julius O. Smith III
{c}
<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.https://music.stanford.edu/people/julius-smith[Department biography, degrees and research area]{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.<Spectral Audio Signal Processing by Julius O. Smith III>[Spectral Envelope Extraction, Cepstral Windowing and equations 11.2–11.3]{ref}
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.
\Image[https://music.stanford.edu/sites/music/files/styles/hs_medium_square_360x360/public/media/capx/julius-smith-square1509507923215.jpg.webp?h=b4e301e9&itok=FqLeCspb]
{title=<Julius O. Smith III>, portrait from Stanford's Department of Music}
{description=External image identified on the institutional biography.}
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