Time-frequency methods for nonstationary systems

This work investigates methods for the analysis and synthesis of nonstationary signals using time-frequency distributions and the development of filtering methods in the time-frequency domain. Using the time or the frequency domains individually has limitations in many applications. Analysing the two domains jointly gives the potential to describe complex system operations and to characterise nonstatioanry phenomena. However, most applications are empirical and there is an interest in constructing analytical models of such phenomena. This work addresses the analytic modelling of classes of nonstationary stochastic processes exhibiting linear or nonlinear (frequency modulated) forms. This includes acoustic phenomena with Doppler shifts and vehicle vibrational motion at variable speed. Simulation of such processes is addressed by scaling the independent variable axis or by using operations in the time-frequency plane. For the analysis of nonstationary time dependent systems the two dimensional transfer function of a system has been used. Operations between the time-frequency expansion of an input signal and the two dimensional transfer function of a system are equivalent to filtering in the time-frequency plane. Simple analytic examples explain the basic methods and are applied to simulated and real data. Models of nonstationary system are released parametrically and nonparametrically in the time-frequency domain.