Abstract: Method of encoding speech at medium to high bit rates while maintaining very high speech quality, as specifically directed to the coding of the linear predictive (LPC) residual signal using either its Fourier Transform magnitude or phase. In particular, the LPC residual of the speech signal is coded using minimum phase spectral reconstruction techniques by transforming the LPC residual signal in a manner approximately a minimum phase signal, and then applying spectral reconstruction techniques for representing the LPC residual signal by either its Fourier Transform magnitude or phase. The non-iterative spectral reconstruction technique is based upon cepstral coefficients through which the magnitude and phase of a minimum phase signal are related. The LPC residual as reconstructed and regenerated is used as an excitation signal to a LPC synthesis filter in the generation of analog speech signals via speech synthesis from which audible speech may be produced.