An investigation into statistical methods of signal comparison

"The purpose of this research was to establish a statistical method of determining if two signals were derived from the same source. The work was motivated by the practical need of ascertaining if such a pair of signals was consistent or otherwise with the hypothesis of a common origin. This question has previously been addressed by several authors. More recent work has focussed on a statistical modelling of the signals and the determination as to whether two signals have the same model parameters. An example of such a work is Quinn (2005), which considers the case where the signal may be characterised as an autoregressive (AR) process with additive sinusoids. This thesis attempts to reproduce and extend this work. This thesis also examines a variety of classes of signal to determine if these are suitable candidates for the purposes of effecting signal comparison and common source attribution. The original contributions of this thesis include: 1. The development and evaluation of alternative methods of characterising time series by ARMA models; 2. The characterisation of simulated time series data by a selection of parameterised models, and an assessment as to which of these techniques enable the common source hypothesis to be supported; 3. The fitting of a variety of parametric models to operationally recorded time series data; 4. The determination that operational data is required to be strongly steady state in order to allow parametric characterisation and consequently the evaluation of the common source hypothesis." -- Abstract