Fractional derivative constrained design of FIR filter with prescribed magnitude and phase responses

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In this paper, the designs of fractional derivative constrained FIR filters with prescribed magnitude and phase responses are presented. First, the definition of fractional derivative is reviewed. Then, FIR filters with complex-valued frequency responses are designed by minimizing the integral squares error under the constraint that the actual response and ideal response have several same fractional derivatives at the prescribed frequency point. Finally, the designs of low group delay low-pass filter and Hilbert transformer are demonstrated to show the effectiveness of the proposed design method.