Design of FIR fractional delay filter based on maximum signal-to-noise ratio criterion

In this paper, a new approach to the design of digital FIR fractional delay filter with consideration of noise attenuation is presented. The design is based on the maximization of signal-to-noise ratio (SNR) at the output of the fractional delay filter under the constraint that actual frequency response and ideal response have several same derivatives at the prescribed frequency point. The optimal filter coefficients are obtained from the generalized eigenvector associate with maximum eigenvalue of a pair of matrices. Numerical examples are demonstrated to show the proposed method provides higher SNR than the conventional FIR fractional delay filter design methods without considering the noise attenuation.