Statistics of the instantaneous interaural parameters for dichotic tones in diotic noise (N(0)S(ψ))

Stimuli consisting of an interaurally phase-shifted tone in diotic noise—often referred to as N(0)S(ψ)—are commonly used to study binaural hearing. As a consequence of mixing diotic noise with a dichotic tone, this type of stimulus contains random fluctuations in both interaural phase- and level-difference. We report the joint probability density functions of the two interaural differences as a function of amplitude and interaural phase of the tone. Furthermore, a second joint probability density function for interaural phase differences and the instantaneous cross-power is derived. The closed-form expression can be used in future studies of binaural unmasking first to obtain the interaural statistics and then study more directly the relation between those statistics and binaural tone detection.