Wavelet Packet Thresholding and Spectrum Estimation

We consider the recent suggestion that spectrum estimation can be accomplished by applying wavelet denoising methodology to wavelet packet coefficients derived from the logarithm of a spectrum estimate. The particular algorithm we consider consists of computing the logarithm of the multitaper spectrum estimator, applying an orthonormal transform derived from a wavelet packet table to the log multitaper spectrum ordinates, thresholding the empirical wavelet packet coefficients, and then inverting the transform. For a small number of tapers suitable partitions/bases for different stationary time series are all similar, and easily derived, and any differences between the wavelet packet and DWT approaches are minimal. For a larger number of tapers, where the chosen parameters satisfy the conditions of a proven theorem, nothing can be gained over the simpler discrete wavelet transform (DWT) thresholding approach. We thus conclude that the DWT approach is a very adequate wavelet-based approach, and that nothing substantial will be gained by using more complicated wavelet packets.