The discrete-time frequency warped wavelet transforms

In this paper we show that the dyadic wavelet transform may be generalized to include non-octave spaced frequency resolution. We introduce orthogonal and complete wavelets whose set of cutoff frequencies may be adapted, in the simplest case, by changing a single parameter. The novel wavelets and the FWWT transform computational structure are obtained via an intermediate Laguerre representation of the signal. The warped wavelets are related to the ordinary wavelets by means of frequency transformations and orthogonalizing filtering. The classical sampled filter bank theory is extended to include frequency dependent upsampling and downsampling operators and dispersive delay lines. The FWWT frequency band flexibility may be exploited in order to adapt the wavelet transform to signals.