A NEW METHOD OF ESTIMATING COMPACTLY SUPPORTED WAVELET WITH DESIRED SUPPORT AND VANISHING MOMENTS FROM A SIGNAL

摘要

In the last decade or so, a large number of researchers have focused their attention on estimation of wavelet matched to a given signal. This paper proposes a new method for estimating compactly supported wavelet from a given signal. The method is based on maximizing the projection of a given signal onto the scaling subspace. This results in energy minimization of the signal in the wavelet subspace so that it can be considered as additional/finer information in the wavelet subspace. Based on this approach, first the analysis wavelet filter is extracted from given signal. Next, analysis scaling filter and synthesis filters are designed such that resulting 2-Band filter bank structure consists of FIR filters that satisfy the property of perfect reconstruction. This leads to the design of compactly supported wavelet. The proposed method is very simple and it is shown that a wavelet, with desired support as well as desired number of vanishing moments, can be designed from a given signal. Simulation results to validate the theory are presented for I-D signals.