Time and frequency representation of acoustic signals by means of the Wigner distribution function: Implementation and interpretation

Abstract

The Wigner distribution function, originally introduced in quantum mechanics, is shown to have a similar formulation as the Fourier transform of the time-dependent correlation function for a time-varying signal. Review of its mathematical properties indicates that such an expression is suitable for representing the signal simultaneously in the time and frequency domains. Furthermore, reformating the Wigner distribution function with a certain window function leads to a proof that this modified version, the pseudo-Wigner distribution function, always has a positive value and hence can be interpreted as a proper description of the dynamics for the signal’s power density spectrum change with time. The implementation of the Wigner distribution function for digital processing can be carried out simply by adapting the fast Fourier transform algorithm. Examples of its application to several types of acoustic signals are used to illustrate their dynamic features jointly in time and frequency representation.