Non-Stationary Sinusoidal Analysis

Many types of everyday signals fall into the non-stationary sinusoids category. A large family of such signals represent audio, including acoustic/electronic, pitched/transient instrument sounds, human speech/singing voice, and a mixture of all: music. Analysis of such signals has been in the focus of the research community for decades. The main reason for such intense focus is the wide applicability of the research achievements to medical, financial and optical applications, as well as radar/sonar signal processing and system analysis. Accurate estimation of sinusoidal parameters is one of the most common digital signal processing tasks and thus represents an indispensable building block of a wide variety of applications.

Classic time-frequency transformations are appropriate only for signals with slowly varying amplitude and frequency content - an assumption often violated in practice. In such cases, reduced readability and the presence of artefacts represent a significant problem. Time and frequency resolution cannot be increased arbitrarily due to the well known time-frequency resolution trade-off by Heisenberg.

The main objective of this thesis is to revise and improve existing methods, and to propose several new approaches for the analysis of non-stationary sinusoids. This dissertation substantially contributes to the existing sinusoidal analysis algorithms: a) it critically evaluates and disseminates in great detail current analysis methods, b) provides significant improvements for some of the most promising existing methods, c) proposes several new approaches for analysis of the existing sinusoidal models and d) proposes a very general and flexible sinusoidal model together with a fast, direct estimator.