Respective samples of input speech data are transformed by a discrete Fourier transformer to obtain a spectrum of the speech data. Simultaneously, values of times of the respective samples are multiplied with the input speech data by a multiplier and a differential spectrum is obtained by transforming a result of the multiplication by a discrete Fourier transformer. A real part of a value obtained by dividing the differential spectrum by the spectrum by a quotient real part calculator and the real part is inverse-transformed by a discrete inverse Fourier transformer. The result of the inverse-transformation is divided by the values of the times of the respective samples to obtain a time function corresponding to phase. On the other hand, a time function corresponding to a logarithmic amplitude spectrum is obtained from an output of the inverse-Fourier transformer by means of a logarithmic amplitude spectrum calculator. A complex cepstrum is obtained by adding the both time functions at respective times by an adder.