Wavelets filter banks based on continuous-time asymptotic filters

Digital signal processing has played a key role in development of telecommunication systems over the last decade. In recent years digital filter banks have been occupying an increasingly important role in wireless and wireline communication systems. In some applications it is necessary to use filter banks which are not uniform. These decompose a given spectrum into sub-spectra of different bandwidths. Filter banks with exponentially spaced center frequencies and bandwidths are of particular interest. The best known examples of this type are octave filter banks, which are considered here. Closely related to these are dyadic wavelets, which are transformation kernels used for multiresolution analysis of non-stationary signals, the so-called wavelet analysis. In this paper an obvious and straightforward idea of wavelet transform construction and building of the corresponding digital filter bank based on a class of finite order error signal energy optimal IIR filters called asymptotic filters are presented and illustrated by simulation