Sound reinforcement systems and loudspeaker arrays consist of numerous, spatially distributed sources. The signal alignment of these components is crucial to provide even level coverage and consistent spectral distribution throughout the audience areas. One usually assumes that sources located close to each other sum coherently in contrast to sources spaced far apart which sum energetically at the receiver. However, in reality this assumption seldom holds since environmental conditions, such as fluctuations of temperature and air flow and their spatial correlation, determine the actual level of coherence. We derive a theoretical framework for practical estimates of this important effect based on stochastic theory. We quantify the resulting measure of coherence as a function of the different environmental parameters in the form of a gradually modified complex amplitude superposition. Results are verified using numerical models and measurement.
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