It has been observed by several authors that a number of different optimum receiving filters (corresponding to different criteria of goodness) for sampled-data transmission systems can be factored as a product of a matched filter and a periodic filter with the period equal to the sampling frequency. By a simple argument it is shown in this correspondence that any reasonable criterion of goodness will lead to an optimum filter that has this form.
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T. Ericson (1971) studied this question.
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