As mentioned in §G.7, the phase vocoder had become a standard analysis tool for additive synthesis (§G.8) by the late 1970s [186,187]. This section summarizes that usage.
In analysis for additive synthesis, we convert a time-domain signal into a collection of amplitude envelopes and frequency envelopes (or phase modulation envelopes ), as graphed in Fig.G.12. It is usually desired that these envelopes be slowly varying relative to the original signal. This leads to the assumption that we have at most one sinusoid in each filter-bank channel. (By ``sinusoid'' we mean, of course, ``quasi sinusoid,'' since its amplitude and phase may be slowly time-varying.) The channel-filter frequency response is given by the FFT of the analysis window used (Chapter 9).
The signal in the subband (filter-bank channel) can be written
Typically, the instantaneous phase modulation is differentiated to obtain instantaneous frequency deviation: