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A method is suggested for improving the response of a symmetric nonrecursive digital filter using several copies of that filter. This is based on shifting and/or scaling the amplitude change function (ACF). A new generalized ACF has been derived which has similar characteristics as that of the Kaiser-Hamming--Chebyshev ACF, but does not require additional correction filters for its implementation. Shifting and scaling of the new ACF are shown to result in further improvement of the response.