IMPLEMENTATION OF OPERATORS VIA FILTER BANKS - HARDY WAVELETS AND AUTOCORRELATION SHELL

We consider implementation of operators via filter banks in the framew ork of the multiresolution analysis. Our method is particularly effici ent for convolution operators. Although our method of applying operato rs to functions may be used with any wavelet basis with a sufficient n umber of vanishing moments, we distinguish two particular settings, na mely, orthogonal bases and the autocorrelation shell. We apply our met hod to evaluate the Hilbert transform of signals and derive a fast alg orithm capable of achieving any given accuracy. We consider the case w here the wavelet is the autocorrelation function of another wavelet as sociated with an orthonormal basis and where our method provides a fas t algorithm for the computation of the modulus and the phase of signal s. Moreover, the resulting wavelet may be viewed as being (approximate ly, but with any given accuracy) in the Hardy space H-2(R). (C) 1996 A cademic Press, Inc.