WAVELET TRANSFORMS FOR DISCRETE-TIME PERIODIC SIGNALS

Wavelet transforms for discrete-time periodic signals are developed. I n this finite-dimensional context, key ideas from the continuous-time papers of Daubechies and of Cohen, Daubechies and Feauveau are isolate d to give a concise, rigorous derivation of the discrete-time periodic analogs of orthonormal and symmetric biorthogonal bases of compactly supported wavelets. These discrete-time periodic wavelets are expresse d in terms of circular FIR filters, and thus lead to fast wavelet tran sforms whose complexity is order N.