Least squares estimation of acoustic reflection coefficient

Abstract

The work presented in this thesis develops further the two-microphone transfer function method used for the measurement of acoustic reflection coefficient of a porous material in an impedance tube.  With the use of a least squares solution, the measurement of the transfer functions between multiple microphones can be used to produce an optimal estimation of reflection coefficient.  The advantage of using this technique is to extend the frequency range of broadband measurements.  The limitations of using the two-microphone transfer function method are analysed in terms of the microphone separations that dictate the upper frequency limit of measurements and it is shown how the measurement of multiple transfer functions can assist in extending the frequency range.  Least squares estimation with multiple transfer functions is also applied to free-field measurements based on an image source model of the reflection process.  The use of an image source model is found to give good results when used with the least squares solution for measurement of reflection coefficient at normal incidence.  Results at oblique incidence seem more difficult to measure accurately in practice because of the precision required in locating microphones.  The use of a reflection model, that is associated with plane wave decomposition, is also introduced although this needs a numerical approach in order to enable the application of least squares estimation.  The numerical process is demonstrated in a simulation that suggests this technique may ultimately be of practical use.

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