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This paper investigates the application of multi-resolution wavelet and cosine packet decompositions to the removal of noise from nonstationary signals. A unique algorithm is developed that selects between wavelet and cosine packet decompositions based on the decomposition entropy. The algorithm pre-whitens, segments, and decomposes the signal into both wavelet transform packets and cosine transform packets, then applies a nonlinear threshold to remove noise prior to apply the inverse transform. Simulations are provided that display the results of the algorithm on two different whale songs.