ESTIMATION OF FRACTAL SIGNALS USING WAVELETS AND FILTER BANKS

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter mas recently proposed for signal restoration and for signal smoothing of 1/f family of fractal signals corrupted b y external noise. The conclusions obtained in these papers are based o n the following simplificative hypotheses: 1) The wavelet transformati on is a whitening filter, and 2) the approximation term of the wavelet expansion can be avoided when the number of octaves in the multiresol ution analysis is large enough. In this paper, we shelf that the estim ation of 1/f processes in noise can be improved avoiding these two hyp otheses. Explicit expressions of the mean-square error are given, and numerical comparisons with previous results are shown.