ANALYTIC GENERAL CONSTRUCTION OF WAVELET FILTERS BASED ON TRIGONOMETRIC FUNCTIONS

摘要

A novel method for constructing wavelet filters is described in this paper. The method generates a parameterization of wavelet coefficients based on sines and cosines of a set of angles. The angles sum to π/4, enforcing a total sum condition. The orthogonal wavelet filter coefficients with arbitrary length are constructed. The unified analytic constructions of orthogonal wavelet filters are put forward for filters of lengths 2~(k-1) and 2k respectively. The parameterization is necessary and sufficient for filters of length 2, the method is shown to be sufficient for filter of lengths 2~(k-1). The famous Daubechies filter and some other wavelet filters are tested by the proposed novel method. This method is very useful for the research on wavelet theory and its applications.