Auditory filter with minimum‐uncertainty product between frequency and scale.

Abstract

A scale representation of a signal describes its compression or dilation as a function of time or frequency. Because the frequency scaling properties of cochlear mechanics vary slowly at frequencies above 1–1.5 kHz, a frequency‐scale representation is of particular interest for auditory filters. An auditory filter is constructed based on the analytic signal with the minimum uncertainty product between frequency and scale. Its spectral and temporal properties are analyzed. The complex spectrum of the filter is completely specified as a function of the frequency relative to the center frequency of the filter, the filter $Q,$ and the dimensionless group delay normalized by the number of periods at center frequency. In approximate agreement with basilar‐membrane mechanics and human psychophysics, the frequency of peak spectral amplitude decreases by a half octave as tuning broadens, the spectral amplitude gain increases with sharper tuning, and the dimensionless group delay of the filter is independent of frequency. The peak envelope of the filter impulse response occurs at a time inversely proportional to the peak spectral frequency. Results are obtained on auditory phase perception for tones embedded in chirp maskers. A nonlinear filterbank composed of frequency‐scale filters has potential applications in auditory research and audio engineering.