Show that if h[n] is an (M + 1)-point FIR filter such that h[n] = h[M − n] and H(z0) = 0,then H(1/z0) = 0. This shows that even symmetric linear-phase FIR filters have zeros that are reciprocal images. (If h[n] is real, the zeros also will be real or will occur in complex conjugates.)
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