A composite source is an indexed family of random processes (subsources) together with a switch which chooses from among these processes in a stochastic fashion. Such a source has often been proposed as a model for speech and other processes having piece-wise, or quasi, stationary behavior. Until recently, however, very little has been known about such models from either a theoretical or a practical perspective. In this paper, we consider a speaker/isolated word recognition system derived from a composite source model for speech production. In particular, estimates of the underlying subsources are obtained using a modified data compression algorithm. Switch sequences are then derived from these estimates for each utterance. Finally, switch sequences are compared in the time domain (using Levenshtein's metric) and from a statistical point of view (via variation distance). Both modes of comparison are seen to be highly correlated and produce a recognition procedure with very encouraging results.

Stationary processes whose restrictions are totally bounded in variation distance are shown to be equivalent to the class of tight measures when the alphabet is countable. For uncountable alphabets, total boundedness implies tightness, but the reverse implication need not hold, as shown by example. Necessary and sufficient conditions for the class of Gaussian processes to be bounded totally are presented. An application of these results to universal coding for composite sources is considered.

Weakly minimax universal codes for composite sources whose channel analog has asymptotically decreasing input memory and anticipation (ADIMA) are examined. In particular, weak universal codes of all rates with respect to an arbitrary distortion measure are shown to exist for ADIMA composite sources when the switch processes belong to a\bar{d}-compact class. These results are immediately applicable to universal coding for classes of remote sources.

A necessary and sufficient condition for a source to satisfy the ergodic theorem and the Shannon-McMillan theorem--the two basic mathematical tools of the Shannon theory--is that it be asymptotically mean stationary (AMS). A channel is defined here to be AMS if whenever an AMS input source is connected to the channel, the resulting input/output process is AMS. We develop several characterizations and properties of AMS channels that resemble those of AMS sources. As an application we show that these ideas are useful in characterizing composite sources, and in particular that there exist sources that exhibit distinct short term and long term stationarity properties. Thus "locally stationary" or "quasi-stationary" processes such as those used to model speech waveforms may also be stationary. In addition, some preliminary results on coding for AMS channels are presented.

A quasi-stationary, or composite, source model arises in a variety of practical and theoretical situations: time-division multiplex environments, speech modeling, and in the study of stationary, nonergodic random processes. This paper considers the problem of coding (with respect to a fidelity criterion) for such processes when the collection of modes is fixed but the switch is unknown. Universal-type codes are sought and it is shown that, for any rate R, there exists a sequence of codes with increasing blocklength whose rates approach R and whose distortions (for any switch process) approach the lowest theoretically obtainable. This result is shown to provide theoretical justification for some current findings in speech compression and in template generation for speaker-independent word recognition.

Fixed rate universal block source coding with a fidelity criterion is considered for classes of composite sources with a finite (fixed) set of modes not an unknown switch process. In particular, it is shown that weakly minimax universal codes of all rates with respect to an arbitrary distortion measure exist for such processes.

Limit theorems are proved for the distortion-rate function and the entropy rate of a composite source in the limit of vanishingly slow switch processes. The degree of slowness in switching is measured via weak convergence to the "fixed" position switch model apropos of universal coding.