Construction of warped time-frequency representations on nonuniform frequency scales, Part I: Frames
Nicki Holighaus, Christoph Wiesmeyr · arXiv (Cornell University) · 2014
Abstract. A flexible method for constructing nonuniform filter banks is presented. Starting from a uniform system of translates, a nonuniform covering of the frequency axis is obtained by nonlinear evaluation. The frequency progression is determined by a warping function that can be chosen freely apart from some minor restrictions. The resulting functions are interpreted as filter transfer functions and, combined with appropriately chosen downsampling factors/translation parameters, give rise to a nonuniform 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 the auditory ERB frequency scale and families of filter banks that can be interpreted as an interpolation between linear (Gabor) and logarithmic (Wavelet, ERBlet) frequency scales, closely related to the α-transform. We investigate conditions on the prototype filter and and warping function, such that the resulting warped filter bank forms a frame. In particular, we obtain a simple and construc-tive method for obtaining tight frames with bandlimited filters by invoking previous results on generalized shift-invariant systems. 1.