A realization of wavelet filter bank with adaptive filter parameters

In this paper, an efficient realization of the two-channel wavelet filter bank with adaptive filter parameters is proposed. Described time variant wavelet filter bank is more suitable for analysis of non-stationary signals then fixed banks. Basic convergence and regularity properties of the limit wavelet functions and scales are provided by fixed part of the filter bank. Variable part adapts to the analyzed signal. Proposed filter bank combines sub-band decomposition and parametric modeling. Realization is based on the lifting scheme, derived from a method of fixed wavelet filter bank design. Original Lagrange interpolation of samples in the time domain is modified to an approximation scheme that is recomputed at each step of decomposition. Adaptation criterion is calculated from wavelet coefficients, which is under some restrictions reproducible on the reconstruction side. Wavelet filter banks with adaptive filter parameters can outperform fixed banks in a number of applications.