The original sines+noise analysis method is shown in Fig.10.11 [246,249]. 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.
Tracking Sinusoidal Peaks in a Sequence of FFTs