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An algorithm is discussed which decomposes a noisy composite signal of identical but unknown multiple wavelets overlapping in time. The decomposition determines the number of wavelets present, their epochs, amplitudes, and an estimate of the basic wavelet shape. The algorithm is an adaptive decomposition filter which is a combination tion of three separate filters. One is an adaptive cross-correlation filter which resolves the composite signal from noise by an iteration procedure; this is followed by a wavelet extraction filter which ferrets out the basic wavelet form, and last there appears an inverse filter which achieves decomposition of the composite signal in the time domain. The decomposition algorithm can be applied to echoes and overlapping wavelets which might arise in radar, sonar, seismology, or electro-physiology. The proposed theory has been thoroughly simulated and selected experimental results are presented to demonstrate the technique. These include decomposition of brain waves evoked by visual stimulation.