Discrete versus Continuous Space Averaging in a Reverberant Sound Field

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Abstract
Continuous averaging along a straight line does not always give better results than averaging at discrete points, uniformly spaced at half a wavelength apart along the same path. The continuous average is often a poorer estimate of the true mean than this discrete average. An explanation of this surprising fact is given, in terms of the cross-correlation curve for the sound field, and it is shown that a discrete average can be found that is always better than the continuous average. Averaging in two or three space dimensions is also considered, and the conclusion is reached that a discrete average, being more accurate and easier to obtain than a continuous average, is preferable. Curves are given for the percent probability of the sample mean lying within prescribed bounds of the true mean, for discrete sampling in a limited region in one, two, and three dimensions.

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