Vocoder Analysis

Vocoders decompose a signal into subbands. For each subband, either the magnitude (in the case of the channel vocoder), or the magnitude and phase (for the phase vocoder) is determined.

If we assume that we have at most 1 sinusoid with time varying parameters in each channel, then we can write down the following expression for , the signal in the subband:

In the above expression, is an amplitude modulation term, is a fixed channel center frequency, and is a phase (or frequency) modulation. Using these parameters, we can re-synthesize the signal using the oscillator summation.^11.1Typically, the instantaneous phase modulation is differentiated to obtain instantaneous frequency deviation:

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.