The Effects of Distortions on Linear System Identification and Non-linear Characterisation

The thesis focuses on the identification of linear systems and those non-linear systems which can be represented with purely linear dynamics and a zero memory nonlinearity in cascade. With the systems subjected to stationary Gaussian processes or periodic excitations and with or without external disturbances at the output, the linear dynamics are estimated as non-parametric or parametric models and any non-linearity is characterised through the form of signals appearing at its input and output. The main research of the first part of the thesis is concerned with non-parametric identification of linear systems with finite time stationary white Gaussian data, or finite gain and phase response measurements. The sources of errors leading to the uncertainty of the frequency response function of a system are identified and it is shown that there is a limit to the reduction in the variance when windowing the measured data and block overlap is employed. The direct use of expressions relating phase and gain responses lead to inaccurate results, and modifications to the functions and extrapolation methods are developed to give significant improvement in accuracy. The second part involves non-linear system identification. By using a sinusoidal excitation, it is shown how the phase of a harmonic at the output relative to the input can be used to deduce the position of the non-linearity in relation to the linear dynamics. Two procedures are developed to identify the dynamics and form of non-linearity in the system. Further, it is shown how among a class of discrete time linear models, the auto-regressive moving average with exogenous input (ARMAX) best describes the linear dynamics of a Hammerstein system while a Box-Jenkins (BJ) best describes the linear dynamics of a Wiener system, in a mean square sense. The last part of the thesis gives a review for periodic perturbation signal design. Graphical user interfaces were developed to ease the generation of pseudo random and multilevel multiharmonic signals.