One approach to the problem of representation of speech signals is to use the speech production model in which speech is viewed as the result of passing a glottal excitation waveform through a time-varying linear filter that models the resonant characteristics of the vocal tract. In many applications it suffices to assume that the glottal excitation can be in one of two possible states corresponding to voiced or unvoiced speech. In attempts to design high-quality speech coders at the midband rates, generalizations of the binary excitation model have been developed. One such approach is multipulse (Atal and Remde, 1982) which uses more than one pitch pulse to model voiced speech and a possibly random set of pulses to model unvoiced speech. Code excited linear prediction (CELP) (Schroeder and Atal, 1985) is another representation which models the excitation as one of a number of random sequences or "codewords" superimposed on periodic pitch pulses. In this chapter the goal is also to generalize the model for the glottal excitation; but instead of using impulses as in multipulse or random sequences as in CELP, the excitation is assumed to be composed of sinusoidal components of arbitrary amplitudes, frequencies, and phases (McAulay and Quatieri, 1986).