Frequency-shift-invariant orthonormal wavelet packet representations

It is commonly known that the dyadic structure of wavelet expansions result s in both time- and frequency-translation sensitivity of an input signal. W e develop the first efficient method to reduce frequency-alignment sensitiv ity by introducing a wavelet packet decomposition that is invariant to freq uency shifts of a signal. A frequency-shifted wavelet packet library is pre sented, and an efficient best-basis algorithm is developed to determine the best signal representation among all frequency shifts of a signal. The alg orithm computes all frequency-shifted coefficients in O(N-2) operations, fo llowed by an efficient depth-first tree search of the same complexity.