Analytical expressions for the envelope correlation of narrow-band stimuli used in CMR and BMLD research

Abstract

Analytical solutions are presented for the correlation between the envelopes of certain narrow-band stimuli that are typically used in experiments on binaural unmasking and on Comodulation Masking Release (CMR). These stimuli consist of two maskers with identical envelopes and a signal that is added to one of the maskers. If the two maskers have the same center frequency and are presented to the right and left ear, the stimulus resembles a binaural MoSm condition. If the two maskers have different center frequencies, we have a CMR condition with one flanking band. The solutions for the envelope correlation differ depending on whether the envelope correlation is expressed as normalized cross correlation or as 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 masker level is much higher than the signal level. In this case the envelope cross correlation is approximately equal to the square root of the waveform correlation. It is argued that the different properties of both types of envelope correlation are of relevance for CMR research.