Frequency-Shift-Invariant Orthonormal Wavelet Packet Representations

It is commonly known that wavelet expansions are very sensitive to translation of an input signal due to their dyadic structure. Without proper time alignment of the signal to the decomposition basis vectors, a compact expansion may be unattainable. Recently, work has been done to combat translation sensitivity by determining the best translation-invariant expansion of a signal with respect to a set of bases. However, the dyadic structure of wavelet expansions also results in frequency alignment sensitivity. In this work, we introduce a frequency-shifted wavelet packet library as well as an efficient best basis algorithm for determining the best signal representation among all frequency shifts of a signal.