Why some audio signal short-time Fourier transform coefficients have nonuniform phase distributions

Abstract: The short-time Fourier transform (STFT) represents a window of audio samples as a set of complex coefficients. These are advantageously viewed as magnitudes and phases and the overall distribution of phases is very often assumed to be uniform. We show that when audio signal STFT phase distributions are analyzed per-frequency or per-magnitude range, they can be far from uniform. That is, the uniform phase distribution assumption obscures significant important details. We explain the significance of the nonuniform phase distributions and how they might be exploited, derive their source, and explain why the choice of the STFT window shape influences the nonuniformity of the resulting phase distributions.