Experimental measurements are reported indicating the frequency-dependent coherence (statistical linear dependence) between a white-noise signal measured at an artificial eardrum representative of a headphone listener and the corresponding, white-noise signal measured at various distances from a loudspeaker in a typical listening room. The cross spectrum, used in coherence analysis, defines the complex frequency response of the linear filter that will modify the earphone signal to sound like the loudspeaker in the listening room. At progressively greater distances from the loudspeaker, the coherence function decreases indicating reduced frequency-dependent signal-to-noise ratio, due, most likely, to increased incoherent reverberant sound, so that linear filtering cannot, in general, accurately reproduce the listening-room sound.
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https://aes2.org/publications/elibrary-page/?id=8373
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