The Optimal Dyadic Derivative
classification
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dyadicderivativeanswersapproximationbestbutzerconvolutioncyclic
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We show that the best approximation to the difference operators on the cyclic groups of order $2^n$ by a dyadic convolution operator are the restrictions of a generalized dyadic derivative. This answers a question on the "intuitive" interpretation of the dyadic derivative posed by Butzer and Wagner more than 30 years ago.
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