Investigation into the phase characteristics of transfer functions

The aim of the work reported in this PhD thesis is to investigate the phase accumulation characteristics of transfer functions in different wave fields. The thesis starts with an overview of previous research on the phase of transfer functions in an ideal wave field, either a direct field or a diffuse field. The poles and zeros theory of Lyon [LYON, 1983] is introduced to give the formula for predicting the phase accumulations based upon a statistical analysis. Both computer simulation results and experimental results confirm the theoretical phase predictions for the ideal wave field in beams and plates.

Following the study of phase in ideal wave fields, the phase accumulation in a nonideal wave field, a wave field between a direct field and a diffuse field, is then investigated. The poles and zeros in the transfer function are studied in more detail and the factors, which affect the phase accumulation such as the damping of the structure, the structure size and the source-receiver separation distance, are discussed. It is suggested that the phase accumulation in a non-ideal wave field can be expressed by the number of the non-minimum phase zeros of the transfer function multiplied by -2n plus the contribution from the propagation phase, -kr. Based on this general assumption, five mathematical models for predicting the phase accumulation of both two-dimensional wave fields such as in plates and three-dimensional wave fields such as in rooms are presented. The predicted results from the mathematical models are then compared to the measured results obtained from experiments on plates and measured results in a reverberant room. Possible factors influencing the prediction accuracy, such as the damping measurement accuracy, near field influences, nonactive resonances, the excitation loacation and the poles-zeros statistics, are also discussed.

For experimental verification of the predictions from theoretical models, it is shown that the test frequency FFT resolution is vital to obtain correct phase accumulation in experimental data. The Half Power Bandwidth, frj, is suggested as a criterion to select proper FFT resolution. Taking the factors affecting the prediction accuracy into account, good agreements are generally obtained between the theoretical predictions and the experimental results when the proper FFT resolution is selected.