An optimal auditory filter

The optimality of the peripheral auditory filter is investigated using operator methods applied to a scale representation. A 'gammachirp' function, which consists of a frequency modulated carrier and an envelope of a gamma distribution function, is found to be the optimal auditory filter in terms of minimal uncertainty if the time-scale representation is calculated in the auditory system. The gammatone function is the first-order approximation of the gammachirp function. The gammachirp function has an asymmetrical Fourier power spectrum and fits the psychoacoustic auditory filter shape better than the gammatone function. Wavelet configuration is optimal for the auditory filterbank in terms of invariability in the scale representation. Data for equivalent rectangular bandwidth (ERB) suggest the wavelet gammachirp filterbank is feasible for characteristic frequencies above 800 Hz.