Digital filter design in the quefrency domain

The desired log magnitude and phase responses are realized by approximating the log frequency response (the complex logarithm of the frequency response). Since the log frequency response is represented by its Fourier series in terms of the quefrency response (the cepstrum of the impulse response), the desired log frequency response is approximated by the filter with a finite length quefrency response. The elemental filter presented in this paper has a component of the quefrency response. Therefore, the quefrency response is realized by a cascade connection of the elemental filters for all its quefrency components. The cascade filter provides the best mean-square approximation to the desired log frequency response. By introducing the elemental filter, digital filters can be designed in the quefrency domain. By designing digital filters in the quefrency domain, the best approximation filter for the desired log frequency response can be easily realized.