The Pole Behaviour of the Phase Derivative of the Short-Time Fourier Transform

TL;DR

This paper investigates a unique pole phenomenon in the phase derivative of the STFT, revealing a recurring pattern around zeros that enhances understanding of phase behavior in time-frequency analysis.

Contribution

It provides a detailed numerical and analytical characterization of the pole phenomenon in the phase derivative of the STFT, a novel insight into phase behavior.

Findings

Identifies a recurring pole pattern near zeros of the STFT

Provides a complete analytical explanation of the phenomenon

Enhances understanding of phase derivatives in time-frequency analysis

Abstract

The short-time Fourier transform (STFT) is a time-frequency representation widely used in applications, for example in audio signal processing. Recently it has been shown that not only the amplitude, but also the phase of this representation can be successfully exploited for improved analysis and processing. In this paper we describe a rather peculiar pole phenomenon in the phase derivative, a recurring pattern that appears in a characteristic way in the neighborhood around any of the zeros of the STFT, a negative peak followed by a positive one. We describe this phenomenon numerically and provide a complete analytical explanation.