The original sines+noise *analysis* method is shown in
Fig.10.11 [#!SerraT!#,#!SerraSmith!#]. The processing path along
the top from left to right measures the amplitude and frequency
trajectories from magnitude peaks in the STFT, as in Fig.10.10.
The peak amplitude and frequency trajectories are converted back to
the time domain by additive-synthesis (an oscillator bank or inverse
FFT), and this signal is windowed by the same analysis window and
forward-transformed back into the frequency domain. The
magnitude-spectrum of this sines-only data is then subtracted from the
originally computed magnitude-spectrum containing both peaks and
``noise''. The result of this subtraction is termed the
*residual signal*. The upper spectral envelope of the residual
magnitude spectrum is measured using, *e.g.*, linear prediction, cepstral
smoothing, as discussed in §10.3 above, or by simply
connecting peaks of the residual spectrum with linear segments to form
a more traditional (in computer music) piecewise linear spectral
envelope.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University