A sinusoidal model for the speech waveform is used to develop a new analysis/synthesis technique that is characterized by the amplitudes, frequencies, and phases of the component sine waves. These parameters are estimated from the short-time Fourier transform using a simple peak-picking algorithm. Rapid changes in the highly resolved spectral components are tracked using the concept of "birth" and "death" of the underlying sine waves. For a given frequency track a cubic function is used to unwrap and interpolate the phase such that the phase track is maximally smooth. This phase function is applied to a sine-wave generator, which is amplitude modulated and added to the other sine waves to give the final speech output. The resulting synthetic waveform preserves the general waveform shape and is essentially perceptually indistinguishable from the original speech. Furthermore, in the presence of noise the perceptual characteristics of the speech as well as the noise are maintained. In addition, it was found that the representation was sufficiently general that high-quality reproduction was obtained for a larger class of inputs including: two overpallping, superposed speech waveforms; music waveforms; speech in musical backgrounds; and certain marine biologic sounds. Finally, the analysis/synthesis system forms the basis for new approaches to the problems of speech transformations including time-scale and pitch-scale modification, and midrate speech coding.