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A direct design procedure for nonrecursive digital filters, based primarily on the frequency-response characteristic of the desired filters, is presented. An optimization technique is used to minimize the maximum deviation of the synthesized filter from the ideal filter over some frequence range. Using this frequency-sampling technique, a wide variety of low-pass and bandpass filters have been designed, as well as several wide-band differentiators. Some experimental results on truncation of the filter coefficients are also presented. A brief discussion of the technique of nonuniform sampling is also included.