Spatial Averaging in a Diffuse Sound Field
David M. Lubman · The Journal of the Acoustical Society of America · 1969
Estimation of mean pressure squared in a reverberation room embodies averages over time, frequency, and space. The benefits of space averaging may be expressed by a number Neq—the equivalent number of uncorrelated samples (degrees of freedom) resulting from space averaging. The variance of the estimated mean pressure squared is that due to frequency averaging alone, Vf2, divided by Neq. A method for finding Neq is presented that is based upon knowledge of the spatial covariance function for pressure squared. Results are given for the cases of sampling at discrete locations, and for continuous integration over a straight line traverse. These results are based upon a covariance function that is intended for pure-tone or extremely narrow-band noise excitation. It is shown that Neq for continuous integration along a straight-line traverse of length L is approximately equivalent to that for discrete sampling at half-wavelength intervals on the same line.