Abstract
This thesis summarizes approximately three years of research on signal modelling for the purposes of system identification. Improvements in signal modelling techniques have been encouraged over the years by society's demand for more efficient ways of accessing information. As a consequence, several modelling/compression techniques in both the time domain and the frequency domain have been developed as possible solutions to these problems. Cepstral deconvolution is a frequency domain modelling technique that has been successfully applied to many diverse fields, such as speech and seismic analysis. Thus far, all cepstral modelling performance has been empirical, relying on the judgement of the designer. Therefore a novel method for measuring root cepstral pole-zero modelling performance is proposed, by introducing a cost function applied directly to the root cepstral domain. It is, therefore, possible to demonstrate the optimized modelling of a pole-zero model and show that its performance is superior to that of a FIR Wiener filter and LPC. The optimized modelling of speech data is considered by a special form of the developed cost function. It is demonstrated that the modelling performance of the root cepstral method is superior to that of the real (magnitude) cepstrum and LPC. A novel method of model order identification for use with time domain modelling methods based around z-plane root cepstral plots is also developed and discussed. It is demonstrated that the positions of a model or plant's poles and zeros may be determined by visual inspection of the resulting z-plane plot. However, performance in noise was poor to that of LPC, leading to difficulties when trying to determine the model's order. Finally, an investigation into the poor phase modelling performance of the algorithm when modelling signals comprised of multiple excitations is presented. It is demonstrated that all DFT/FFT based analysis techniques are fundamentally flawed due to discontinuities. As a consequence, a simple pre-filtering algorithm is presented as a possible solution.