An improved voice messaging system using LPC baseband speech coding. In standard LPC-based baseband speech coding techniques, LPC parameters plus a residual signal are transmitted. To save band width, the residual signal is filtered so that only a fraction of its full bandwidth (e.g., the bottom 1 KHz) is transmitted. At the decoding station, this fraction of the residual signal (which is known as the baseband signal) is copied up or otherwise expanded to higher frequencies, to provide the excitation signal which is filtered according to the LPC parameters to provide the reconstituted speech output. However, this tends to produce perceptually significant ringing effects and high frequency distortion in the reconstituted signal. The present invention uses a variable baseband width, which is adaptively varied, in accordance with an integral multiple of the frequency of the pitch of the input signal, to provide a more appropriate harmonic match in the reconstituted excitation signal. This eliminates the noticeable ringing effect.