Frequency-shift-invariant orthonormal wavelet packet representations

It is commonly known that the dyadic structure of wavelet expansions results in both time- and frequency-translation sensitivity of an input signal. We develop the first efficient method to reduce frequency alignment sensitivity by introducing a wavelet packet decomposition that is invariant to frequency shifts of a signal. A frequency-shifted wavelet packet library is presented, and an efficient best-basis algorithm is developed to determine the best signal representation among all frequency shifts of a signal. The algorithm computes all frequency-shifted coefficients in O(N²) operations, followed by an efficient depth-first tree search of the same complexity