A direct approximation technique of log magnitude response for digital filters

A new direct approximation technique of log magnitude response for digital filters is presented in this paper. The facts that the log magnitude response of digital filters can be expanded into Fourier series and a fairly accurate cosine type log magnitude response can be realized by the elemental digital filter presented in this paper are used in the present technique. The system functions obtained by this method provide the best mean-square approximation to an arbitrarily prescribed log magnitude response. The resulting digital filters are realized in the cascade form of the elemental digital filters, and they give relatively low coefficient sensitivity. The elemental filter is recursive but its form is very simple. Its coefficients are easily obtained by the cepstrum of the impulse response which is the Fourier transform of the desired log magnitude response. This method is very powerful in the realization of digital filters for speech synthesis filters with complicated log magnitude responses.