A class of warped filter bank frames tailored to non-linear frequency scales (Q2291576)

The authors constructed a method for non-uniform filter banks starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis. The warping function is a \(C^1\)-diffeomorphism that determines the frequency progression and can be chosen freely. They combined with appropriately chosen decimation factors, a non-uniform analysis filter bank is obtained. They also constructed 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. A simple and constructive method for obtaining tight frames with bandlimited filters is derived by invoking previous results on generalized shift-invariant systems.