Abstract: This invention provides a novel speech coding system which recursively executes a filter-applied "Toeplitz characteristic" by causing a drive signal (i.e., an excitation signal) to be converted into a "Toeplitz matrix" when detecting a pitch period in which distortion of the input vector and the vector subsequent to the application of filter-applied computation to the drive signal vector in the pitch forecast called either "closed loop" or "compatible code book" is minimized. The vector quantization method substantially making up the speech coding system of the invention is characteristically used by the system.