| Cyclical patterns are common in signals that originate from natural systems such as the human body and man-made machinery. Often these cyclical patterns are not perfectly periodic. In that case, the signals are called pseudo-periodic or quasi-periodic and can be modeled as a sum of time-varying sinusoids, whose frequencies, phases, and amplitudes change slowly over time. Each time-varying sinusoid represents an individual rhythmical component, called a partial, that can be characterized by three parameters: frequency, phase, and amplitude. Quasi-periodic signals often contain multiple partials that are harmonically related. In that case, the frequencies of other partials become exact integer multiples of that of the slowest partial. These signals are referred to as multi-harmonic signals. Examples of such signals are electrocardiogram (ECG), arterial blood pressure (ABP), and human voice.;A Markov process is a mathematical model for a random system whose future and past states are independent conditional on the present state. Multi-harmonic signals can be modeled as a stochastic process with the Markov property. The Markovian representation of multi-harmonic signals enables us to use state-space tracking methods to continuously estimate the frequencies, phases, and amplitudes of the partials.;Several research groups have proposed various signal analysis methods such as hidden Markov Models (HMM), short time Fourier transform (STFT), and Wigner-Ville distribution to solve this problem. Recently, a few groups of researchers have proposed Monte Carlo methods which estimate the posterior distribution of the fundamental frequency in multi-harmonic signals sequentially. However, multi-harmonic tracking is more challenging than single-frequency tracking, though the reason for this has not been well understood. The main objectives of this dissertation are to elucidate the fundamental obstacles to multi-harmonic tracking and to develop a reliable multi-harmonic tracker that can track cyclical patterns in multi-harmonic signals. |
