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A STUDY OF THE PERFORMANCE OF LINEAR AND NONLINEAR FILTERS.
MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS
A measure of the performance of filters is proposed which compares the filter under study to an optimum attenuator acting on the same input. The noise level noise-to-message power ratio is emphasized as an independent parameter important to the behavior and the performance of both linear and nonlinear filters. For optimum and nonoptimum linear filters, the effect of the noise level on the performance is the specific object of study. For nonlinear no-memory filters after consisdering the determination of the optimum filter for mean-square and non mean-square criteria, the characteristics of the message and the noise are investigated for which the optimum mean-square filter reduces to an attenuator. At the other extreme of behavior, perfect separation by a nonlinear no-memory filter will not occur for any message of interest, and the selection of the message of a defined class which will give the smallest or largest average weighted error is considered. For a given noise, a given error criterion, and a known filter, messages are considered that have prescribed peak and average power Author