By using a log spectrum approximation filter modeling a true log spectral envelope, a low bit rate and high‐quality vocoder was realized. The true log spectral envelope is represented by the low‐quefrency portion of the cepstrum modified by the low‐quefrency components involved in the rectified fine structure of the log spectrum. It can be obtained through an iteration of DFT‐rectifying‐IDFT for the higher quefrency portion of the speech cepstrum. In this vocoder, the speech synthesis is not based on the homomorphic method. The synthesis filter can be obtained without transforming the cepstrum to an impulse response, and the computation for the filter coefficients is very simple. The spectral envelope information is transmitted in the form of a differential cepstrum corresponding to the difference of two adjacent log spectral envelopes, and the data rate is very low.