A class of warped filter bank frames tailored to non-linear frequency scales

A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function. The warping function is a C^1 -diffeomorphism that determines the frequency progression and can be chosen freely, apart from minor technical restrictions. The resulting functions are interpreted as filter frequency responses and, combined with appropriately chosen decimation factors, give rise to a non-uniform analysis filter bank. Classical Gabor and wavelet filter banks are obtained as special cases. Beyond the state-of-the-art, we construct a filter bank adapted to a frequency scale derived from human auditory perception and families of filter banks that can be interpreted as an interpolation between linear (Gabor) and logarithmic (wavelet) frequency scales. For any arbitrary warping function, we derive straightforward decay conditions on the prototype filter and bounds for the decimation factors, such that the resulting warped filter bank forms a frame. In particular, we obtain a simple and constructive method for obtaining tight frames with bandlimited filters by invoking previous results on generalized shift-invariant systems.

The preprint is available here ltfatnote049.pdf. Note that it might differ from the published version.