The Measurement of In-Situ Absorption Coefficients Using Digital Correlation/Power Spectral Density Techniques

Using the theory of linear systems and stochastic processes, a model of the flat acoustic absorber was devised. By cross-correlating the system input and output, the cross-correlogram is shown to consist of the input autocorrelation function plus the input autocorrelation function convolved with the impulse response of the absorbing material. Proper truncation of the cross-correlogram, coupled with the standard frequency transform/system relations, makes possible the calculation of the frequency response function H(f). For white-noise inputs, the magnitude of H(f) is shown to have a simple relationship to the reflection coefficient, and hence enables the calculation of α, the absorption coefficient. Using a digital correlator whose correlation functions were Fourier transformed on the computer, system response functions for several common building materials were measured in an anechoic chamber. From these data, the reflection and absorption coefficients were calculated. Although the method is generally applicable to any angle, data are only presented for normal incidence. Measurements were also made in more complicated acoustic environments to test the general engineering applicability of the method.