Application of cepstral techniques to the measurement of reflection coefficients for dispersive systems

Khalili, Nasser (1991) Application of cepstral techniques to the measurement of reflection coefficients for dispersive systems. University of Southampton, Doctoral Thesis.

Abstract

The aim of this thesis is the determination of the reflection coefficients arising in dispersive systems. The proposed method relies on a single measurement and makes use of the cepstral deconvolution techniques. The novel feature of the technique is that requirements for the direct and reflected waves to be separable in the time domain are removed and furthermore, they are allowed to overlap in time. In non-dispersivesystems the reflection coefficients have been measured using the cepstral techniques, however, in situations where the propagating waves are dispersive, e.g., a beam or pipe with discontinuities, the reflection coefficient cannot be estimated using the above technique. This thesis describes how the cepstral method may be extended to accommodate this. The basis of the method is the incorporation of the dispersion relation into the power cepstrum analysis of a signal comprised of a direct wave and one or more reflections from the reflectors. This results in a cepstrum in which the independent variable is space such that at a point determined by the distance between the measurement and the reflector, a function related to the reflection coefficient appears. Different functions appear in the cepstrum corresponding to different types of discontinuities. The technique is based on the direct extraction of this function from the remainder of the cepstrum and by taking its Fourier transform, the reflection coefficient of the reflector is then obtained. For the flexural wave propagation in a rectangular cross-section beam, where different types of discontinuities were considered, the determination of the reflection coefficients have been mathematically formulated. Computational results are then presented together with experimental results. For our frequencies of concern (i.e., ≤ 1000 Hz), the estimated reflection coefficients matched with theory and from the cepstrum, the length of path the wave travelled along the beam can also be obtained. The technique has also been applied to multi-mode systems (having more than one dispersion relation), and experimental results are obtained for acoustic wave propagation along the interior of a rigid-walled pipe (or duct) with one end open. For propagation of plane wave, good agreement has been obtained between the measured and theoretical reflection coefficient of the open end. For frequencies above the first cut-off value, a logical approach was to consider the dominant mode.

This record has no associated files available for download.

Contributors

Download statistics