Design of minimum-phase digital filters as the sum of two allpass functions using the cepstrum technique

A new and practical approach using the cepstrum technique is proposed in the design of minimum-phase digital filters as the sum of two allpass functions. The desired magnitude response is specified in the frequency domain. Its corresponding minimum-phase response is then obtained from the desired magnitude response. The desired phases for the two allpass filters are obtained from the magnitude and phase responses. For both filters to be stable, the corresponding denominator polynomials are minimum phase. The filter coefficients are obtained from the desired phases using the cepstrum technique. Design examples show that the method works well for both classical filter specification and general magnitude specification in the frequency domain.