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A time-domain method is presented for designing nonrecursive digital filters that are optimum in the sense that the output samples are least mean-square estimates of the samples of some desired signal. The method requires that one know the input autocorrelation function and the cross-correlation function between the input and the desired output. Several examples are given of filters designed by the method. The optimum filters can be obtained by sampling the impulse responses of optimum filters for continuous reconstruction of the waveforms from their samples.