Application of cepstral techniques to the automated determination of the sound power absorption coefficient

Master Thesis


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University of Cape Town

This thesis builds on research by Bolton and Gold, who developed the theory of using cepstral analysis to determine the absorption coefficient of elastic porous materials. Jongens, in his Masters thesis, applied this technique to determine the absorption coefficient of asphalt samples mounted in a sample holder at the end of a tube. Jongens and others identified numerous factors that introduced uncertainties into the measurement. These uncertainties fall into two main categories. The first deals with the influences that the links of the measurement chain have on the ability to separate the incident and reflected signal. The second deals with the influence of the air leakage between the tube and the surface under measurement in-situ. This thesis deals with the first category. The objectives of this project are to continue the work of Jongens, to produce an apparatus that can rapidly determine the sound power absorption coefficient by a non-skilled operator in a noisy environment. The results should correlate closely with the standardised impedance tube method, within 0.05 over the range 200 Hz to 2000 Hz. The constraint that the apparatus be usable by a non-skilled operator means that little or no calibration should be required, nor should the microphone need to be handled. This thesis presents a survey of related methods used to determine the sound power absorption coefficient. Theory of the cepstral technique is discussed, along with methods that could be used to improve the accuracy of the technique. Excitation signals that could be used with the cepstral method are put forward. The Inverse Repeat Sequence (IRS) was used to excite the system. It was chosen for its high noise immunity, as well as its complete odd-order non-linearity immunity. Sources of uncertainties from the links of the measurement chain are considered and methods to overcome them are presented. Issues that arise from liftering - cepstral equivalent of windowing - are then highlighted. The apparatus for the cepstral technique and method of standing wave ratios used to determine the absorption coefficient is given. The results obtained using the cepstral technique are correlated with the impedance tube results. It was found that the cepstral method correlates closely with the impedance tube over the range of 200 Hz to 2000 Hz for a wide variety of samples. The apparatus was developed to be used by a non-skilled operator, only requiring the press of a button to perform the measurement. With the high noise immunity of the IRS signal, the measurement could be carried out in a noisy environment.

Includes bibliographical references.