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At 7:29 AM 9/26/96, Galembo Alexandre wrote [with my interpretive edits]:
>I would like to find the simplest and most effective way to do the following
>operations with musical signals:
>1. to warp the frequency scale of the spectra (using some formula),
> preserving the time envelope for each spectral component.
>2. Reproduce the sound in the new scale.
Once you identify "each spectral component" it is trivial: each "sinusoidal"
component consists of a time-varying frequency and a time-varying amplitude,
so just warp the frequency, regenerate the modulated sinusoids, and add them up.
The hard part, as with many sound processing schemes that rely on the notion
of spectral components, is to decompose a sound into a discrete set of
modulated spectral components. Quatieri and others have done a lot on this
topic, so I won't try to tell you how to do it. But be careful, because a
scheme that works pretty well for analysis and resynthesis without warping the
frequency scale may not work so well when you include such modifications.
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