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A class of procedures for detection of a pulsed signal having unknown frequency shift is described. From this class, procedures can be selected whose detection performance approximates that of coherent detection arbitrarily closely. Such procedures do not require the construction of a filter bank; on the other hand, they do not yield information as to the magnitude of the frequency shift of a detected signal. Envelope detection followed by video integration, and Reed's so-called semicoherent procedure are elements of this class of detection procedures. An iterative method for obtaining successively better approximations to coherent detection is described, the implementation of which would require a large number of mixing and delay operations. The number of iterations required to insure any given degree of approximation to coherent detection, for any number of integrated pulses, is estimated. Finally, the possible application of these ideas to reception of signals by array antennas is described.