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

TL;DR

This paper investigates the nonuniform phase distributions of STFT coefficients in audio signals, revealing that the common assumption of uniform phase distribution often overlooks important details and is influenced by window shape.

Contribution

It demonstrates that STFT phase distributions are often nonuniform across frequency and magnitude ranges, challenging the standard uniform assumption and explaining the influence of window shape.

Findings

STFT phase distributions can be far from uniform in audio signals

The choice of window shape affects phase distribution nonuniformity

Nonuniform phases contain significant information that can be exploited

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.