Abstract: The present invention relates to method and device for coding speech and to method and device for inverse-quantizing signals coded by the speech coding method. The object of the present invention is to realize an improved coding accuracy and an improved predictive gain by using a correlation between frames of a spectrum, if necessary, in an coding step. A first filter uses a coefficient determined by a predictive coefficient analyzed in a previous frame. After an input speech signal is subjected to a inverse filtering process by the first filter, the first predictive residual signal obtained is subjected to a linear predictive coding to obtain a predictive coefficient. A second filter subjects the predictive coefficient to an inverse filtering process and the resultant second predictive residual signal is quantized.