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A technique for decomposing a composite signal, which consists of the superposition of known multiple signals overlapping in time, is described. Decomposition includes determining the number of signals present, their epochs (arrival times), and amplitudes. The procedure is investigated for the noise-free and noisy situation. The computation algorithm employs the fast Fourier transform to determine the decomposition filter from a knowledge of the signal waveshape and the specified pulse output. The latter is used to recognize the signal arrival time; the amplitude of which is proportional to the signal amplitude; and the number of such pulses denotes the number of individual signal waveforms that make up the composite signal. Digital data processing problems such as filter realizability, signal resolution capability, the effects of additive noise, frequency (spectrum) compatibility between signal waveform and filter response pulse, and possible additional processing in certain cases are discussed. Applications are decomposition or resolution of signals or echoes in radar and sonar, seismology, brain waves, and neuroelectric spike data. Examples of results are presented for decomposition for noiseless and noisy cases for specified signals. In addition, results are tendered for the decomposition of brain waves evoked by visual stimulation.