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:
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(G.4) |