Abstract

Wavelet packets were introduced by Coifman, Meyer and Wickerhauser by generalizing the link between multiresolution approximations and wavelets. Different types of time-frequency structures are encountered in complex signals, such as speech recordings. This motivates the design of bases whose time-frequency properties may be adapted. Wavelet bases are one particular family of bases that represent piecewise smooth signals effectively. Other bases are constructed to approximate different types of signals such as highly oscillatory waveforms. Orthonormal wavelet packet bases use conjugate mirror filters to divide the frequency axis in separate intervals of various sizes. If the signal properties change over time, it is preferable to isolate different time intervals with translated windows. Local cosine bases are constructed by multiplying these windows with cosine functions. Wavelet packet and local cosine bases are dual families of bases. Wavelet packets segment the frequency axis and are uniformly translated in time. Whereas, local cosine bases divide the time axis and are uniformly translated in frequency.

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