1. In signal processing apparatus including means implementing both vocoder and modem functions in a half duplex mode of operation in response to a voice signal in a transmit mode and a modem signal in a receive mode, the improvement comprising: input means selectively coupled to the voice signal and the modem signal to provide respective digital data sequences therefrom; common computer means coupled to said input means implementing a single fast Fourier transform algorithm adapted to perform a first multi-point complex fast Fourier transform in the transmit mode and to perform a second multi-point complex fast Fourier transform in the receive mode, said first transform being operable to effect spectrum and cepstrum analysis of the digital data sequence of the voice signal to provide pitch detection and cepstral encoding signals therefrom, and said second transform being operable to effect demodulation of the digital data sequence of the modem signal to provide pitch and impulse response signals therefrom; first circuit means coupled to said common computer means in the transmit mode and being responsive to the pitch detection and cepstral encoding signals to generate a plurality of information bearing tone waveforms to provide a modem signal in digitized form; first feedback circuit means connected to the output of said common computer means for feeding back a processed spectrum signal in the transmit mode to the input of said common computer means; second circuit means coupled to said common computer means in the receive mode and being responsive to the pitch and impulse response signals to generate an output speech waveform in digitized form; second feedback means connected to the output of said common computer means for feeding back a processed spectrum signal in the receive mode to the input of said common computer means; and output means selectively coupled to said first and second circuit means in synchronism with said input means to provide an analog signal of either a modem signal in the transmit mode or a voice signal in the receive mode.