OPTIMIZING THE ALGORITHM OF THE WAVELET PACKET SIGNAL FILTERING

Abstract

A wavelet packet filtering algorithm has been developed, which includes cyclic movement along the branches of the wavelet packet tree with a constraint on each branch of the approximation and detail coefficients until the minimum root-mean-square error is attained, with the optimal parameters of the wavelet threshold and threshold function. To calculate the root-mean-square error of filtering, after each cycle of processing the wavelet decomposition coefficients, the signal is reconstructed in the time domain. In the next cycle, the received signal is decomposed into approximation and detail coefficients until the root-mean-square error reaches a minimum for all possible values of the basic wavelet-threshold and the threshold function. The study was conducted with twenty of the most commonly used signals, including signals with linear and non-linear frequencies. To confirm the efficiency of packet wavelet filtering, a comparative analysis with the known methods based on a common threshold of detail coefficients at all levels of wavelet decomposition is given. Keywords: wavelet analysis, packet wavelet filtering, entropy, threshold function, threshholding.