In the 1970s, the phase vocoder was reimplemented using the FFT for increased computational efficiency by Portnoff [195]. The FFT window (analysis low-pass filter) was also improved to yield exact reconstruction of the original signal when synthesizing without modifications. Shortly thereafter, the FFT-based phase vocoder was adopted as the analysis method of choice for additive synthesis in computer music [169]. Since then, numerous variations and improvements of the phase vocoder have appeared, e.g., [86,199,124,122,126,125,123]. For an excellent introductory tutorial, see [55]. A summary of vocoder research from the 1930s to the 60s appears in a review article by Manfred Schroeder [223].
Section 10.3 gives further details about classic vocoder processing.