Time frequency modelling

The overriding aim of this thesis is to investigate the benefits of focusing time-frequency analysis on particular regions of the time-frequency plane. The thesis examines aspects of such a regionalisation in the analysis of both deterministic signals and stochastic processes. The majority of deterministic energetic time-frequency representations are non-parametric indicating the distribution of the energy of a signal in the time-frequency plane but providing no further information about the time-frequency structure. This thesis develops a semi-parametric time-frequency model to simultaneously describe the time-frequency energetic structure of a signal and provide an indication of its time-frequency complexity. The model aims to identify ‘timefrequency components’ within the signal to indicate how their energy is distributed in the time-frequency plane and thereby to probabilistically associate every location in the plane with each identified component. The thesis investigates a number of applications of the model including time-frequency decomposition noise reduction and the design of perfect reconstruction filter banks. The model is also used to generate regionally optimised time-frequency distributions. The thesis develops a framework for regional time-frequency analysis of non-stationary random processes and LTV systems defining the class of ‘regionally underspread’ processes and systems and developing approximate regional transfer function relationships. The framework is used to define a measure of the strength of the linear relationship between two regionally underspread processes in a specific region of the time-frequency plane. The measure termed ‘regional coherence’ is useful when the linear relationship remains consistent over a time-frequency region. The time-frequency model and the regional coherence measure are both used in the analysis of slow wave potentials recorded from the motorcortex of a monkey during the execution of a motor task.