Reduced interference distribution application and interpretation for transient acoustic events

Abstract

Transient acoustic events often present difficulties when using conventional time-series or spectral methods. The Reduced Interference Distribution (RID) and its derivatives have been under development [W. J Williams and J. Jeong, Time-Frequency Signal Analysis, edited by B. Boashash (Longman Cheshire, New York, 1992)] for several years. The RID was specifically motivated by the need for a better analysis tool for transient acoustic events [ONR Grants N00014-90-J-1654, N00014-97-1-0072]. The deficiencies of the spectrogram for marine mammal sound analysis were early recognized [William Watkins, Marine Bioacoustics 2, 15–43 (1966)]. Watkins’ illustrations of spectrogram deficiencies and updated results obtained using the Wigner distribution (WD) and the RID will be presented. The RID represents an attempt to retain the desirable mathematical properties of the WD while reducing the often troublesome WD interference terms. Examples drawn from several acoustic transients such as marine mammal sounds, joint clicks and vortex formations in turbulent air flow will be used to illustrate the usefulness of the RID approach. The importance of retaining such properties as proper time and frequency marginals; time and frequency support along with proper group delay and instantaneous frequency will be discussed. The value of covariance with time and frequency shifts and scale changes will also be emphasized.