Coherent Demodulation of Nonstationary Random Processes

Abstract

Nonstationary processes have local properties which change over time. An example is speech, which can be represented as pitch harmonics multiplied by slower-varying syllabic modulations. Commonly-used power spectral analysis reveals the relative intensity of harmonics, but not their relative phase alignment. From an estimation standpoint, speech harmonics are random and thus not perfectly periodic. Syllabic modulations, at a longer time scale, are also ordered yet aperiodic. Instead, their relative alignment can be described as ``rhythmic.'' This thesis shows how a type of rhythm manifests as conjugate correlations in the frequency domain, a phenomenon called impropriety. A useful aspect of impropriety is its algebraic structure, which provides a new maximum-likelihood framework for synchronous estimation. Interestingly, impropriety can also appear in non-harmonic processes, such as underwater propeller noise. This suggests possible generalizations of rhythm and synchrony to a broader class of signals beyond speech. For this class, frequency-domain impropriety can be modeled in terms of linear systems with quickly time-varying subcomponents. Rather than impede analysis, these time variations provide a synchronization cue for coherent demodulation analysis of signals which are highly nonstationary.