Signals and noise
Morgan Jay Arnold · Science & Engineering Faculty · 1996
The broad-based goal of this thesis is to understand, detect, identify and quantify the abstract entity in noise. In general this will be guided by the motivation to extract some form of underlying information, or signal, from what we observe. Specifically this will involve signal and noise modelling, tackling some of the unresolved issues of signal processing including analysis of non-stationary and multicomponent signals non-Gaussian noise. Some philosophical background is formulated which explains what ·we mean by the notions of signal and noise that ·we are using. This lays the foundation for some more specific investigations of signal models, noise models and analysis techniques. Polynomial models for the phase of an analytic signal are first investigated and utilised to optimise some time- domain instantaneous frequency estimation techniques. These techniques, based on phase differencing, significantly improve performance over traditional methods, such as the central finite difference. A new philosophy towards signal filtering, termed time-frequency peak filtering, is presented. This method is shown to enhance signals in high noise environments, preserving frequency content far below normal noise thresholds. Good results are obtained for a broad range of non-stationary (general) signals. The effects of non-Gaussian noise are accounted for by utilising higher-order cumulant information, specifically with a new methodology called higher-order probability distributions. Then we propose to model random variables using characteristic functions and derive an estimation scheme for these quantities based on kernel functions. As a practical application this methodology is applied to the problem of testing for Gaussianity with results comparative to the best known of such tests.