The least-squares invertible constant-Q spectrogram and its application to phase vocoding.

This paper discusses the development of a constant-Q spectrogram representation that is invertible in a least-squares sense. A good quality inverse is possible because this modified transform method, unlike the usual sliding window constant-Q spectrogram, does not discard data samples when performing the variable length discrete Fourier transforms on the signal. The development of a phase vocoder application using this modified technique is also discussed. It is shown that a phase vocoder constructed using the least-squares invertible constant-Q spectrogram (LSICQS) is not a trivial extension of the regular FFT-based phase vocoder algorithm and some of the mathematical subtleties related to phase reassignment are addressed.