Comparative analysis of adaptive wavelet-packages algorithms

The basic versions of adaptive algorithms for wavelet-transformations bases are considered. The orthogonal wavelet-transformations adaptability is defined as an automatic choice of signal basis in both the frequency and the space domains. The algorithms of space and frequency localization of two-dimensional wavelet-packages are studied and compared as well as the search of the best basis on trees. The representation of mathematical models used in adaptive signals filtration is given. The following dual bases families are considered: orthonormal wavelet-packages bases dividing the frequency axis into segments and uniformly shifted in time; local cosine bases, uniformly frequency-shifted and dividing the time axis. The comparison of adaptive wavelet-packages algorithms is made: the number of bases searched through by each algorithm and computational complexity. It should facilitate the basis choice for a particular wavelet-package application in practice.

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