Phase Vocoder Sinusoidal Modeling

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

In this expression, is an amplitude modulation term, is a fixed channel center frequency, and is a

Typically, the instantaneous phase modulation is differentiated to obtain instantaneous frequency deviation:

(G.4) |

The analysis and synthesis signal models are summarized in Fig.G.9.

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