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Auditory Filter Banks

Auditory frequency-scale warping is closely related to the topic of auditory filter banks which are non-uniform bandpass filter banks designed to imitate the frequency resolution of human hearing [30,32]. Classical auditory filter banks include constant-Q filter banks such as the widely used third-octave filter bank. More recently, constant-Q filter banks for audio have been devised based on the wavelet transform, including the auditory wavelet filter bank [8]. Auditory filter banks have also been based more directly on psychoacoustic measurements, leading to approximations of the auditory filter frequency response in terms of a Gaussian function [27], a ``rounded exponential'' [29], and more recently the gammatone (or ``Patterson-Holdsworth'') filter bank [30,32]. The gamma-chirp filter bank further adds a level-dependent asymmetric correction to the basic gammatone channel frequency response, thereby providing a yet more accurate approximation to the auditory frequency response [10,9].

All auditory filter banks can be seen as defining some linear to warped frequency mapping, since the filter-bank output signals are non-uniformly distributed versus frequency. While this paper is concerned primarily with approximating the Bark frequency scale using a first-order conformal map, the same approach can be used to approximate the warping defined by any pre-existing auditory filter bank.

As another application of the results of this paper, an alternative to the use of an auditory filter bank is a simpler uniform filter bank, such as an FFT, applied to a signal having a warped spectrum, where the warping is designed to approximate whatever auditory frequency axis is deemed most appropriate. It so happens that the earliest related work we are aware of was concerned with exactly this application, as we take up in the next subsection.

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``The Bark and ERB Bilinear Transforms'', by Julius O. Smith III and Jonathan S. Abel, preprint of version accepted for publication in the IEEE Transactions on Speech and Audio Processing, December, 1999.
Copyright © 2020-07-19 by Julius O. Smith III and Jonathan S. Abel
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University