Measurement and specification of the envelope correlation between two narrow bands of noise

Empirical measurements show that when two independent, narrow-band, Gaussian noises are 'mixed' or combined according to the method specified by Licklider and Dzendolet (1948) [Science, 107, 121-124], the correlation coefficient between the envelopes (rExy) of the two resulting narrow-band noises is approximately equal to the square of the correlation between the waveforms (rxy). This relation also holds for waveform correlations produced by de-correlating two perfectly correlated noises by the addition of a sinusoid (at the center frequency) that is phase-reversed (N0S pi). This is true so long as the signal-to-noise ratio is small. A method is detailed whereby any desired rExy may be achieved with reasonable accuracy between two noises of the same or different center-frequency. This method may prove particularly useful in the study of listeners' sensitivities to dissimilarities in the envelope fluctuation of bands of noise occupying discrete spectral loci, a topic currently of interest. It is hoped that the empirical relations between rxy and rExy may stimulate efforts to derive or locate analytic expressions that relate the two.