The phase vocoder: theory and practice

This article discusses the theoretical principles governing the short time Fourier transform (STFT) and its musical applications, using the CARL phase vocoder and the Composers' Desktop Project (CDP) spectral transformations. The former was originally developed by Dolson (1986, 1991) and ported to personal computer systems by Atkins, Bentley, Henderson, Orton and Wishart (Atkins, Bentley, Endrich, Fischman, Malham, Orton and Wishart 1987, Wishart 1994a). The latter was developed by Wishart (1994b). When possible, theoretical matters are presented in a qualitative way, keeping the number and complexity of mathematical expressions within the essential requirements for those interested in musical applications. The latter are accompanied by sound examples, including excerpts from pieces by the author.