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An eigenfilter approach is presented for designing 1-D and 2-D variable fractional delay FIR and all-pass filters. First, the coefficients of filters are expressed as a polynomial of the fractional delay parameter. Then, the optimal polynomial coefficients are obtained from the elements of the eigenvector corresponding to the minimum eigenvalue of a real, symmetric and positive definite matrix. Finally, several design examples of 1-D and 2-D variable fractional delay FIR and all-pass filters are used to illustrate the effectiveness of the eigenfilter approach.