Shift invariant wavelet packet bases

A shifted wavelet packet (SWP) library, containing all the time shifted wavelet packet bases, is defined. A corresponding shift-invariant wavelet packet decomposition (SIWPD) search algorithm for a “best basis” is introduced. The search algorithm is representable by a binary tree, in which a node symbolizes an appropriate subspace of the original signal. We prove that the resultant “best basis” is orthonormal and the associated expansion, characterized by the lowest “information cost”, is shift-invariant. The shift-invariance stems from an additional degree of freedom, generated at the decomposition stage, and incorporated into the search algorithm. We prove that for any subspace it suffices to consider one of two alternative decompositions, made feasible by the SWP library. The computational complexity of SIWPD may be controlled at the expense of the attained information cost, to an extent of O(2Nlog₂N)