Analytical expressions for the envelope correlation of certain narrow-band stimuli

Abstract

Analytical solutions are presented for the correlation between the envelopes of certain narrow-band stimuli which are typically used in binaural research. These stimuli are either the sum of an in-phase masker and an out-of-phase signal, or they are two partially correlated noises. Because an envelope has a nonzero mean, the solutions differ depending on whether the envelope correlation is expressed as the normalized cross correlation or as the normalized cross covariance (Pearson product-moment correlation). The envelope correlation depends on the statistics of the masker and the signal whereas the waveform correlation depends on neither. This influence only disappears for the normalized envelope cross correlation provided that the correlation is close to one. In this case, the normalized envelope cross correlation is equal to the square root of the waveform correlation. The results for two partially correlated noise bands are also of relevance for experiments dealing with monaural envelope discrimination and comodulation masking release.