Modeling the temporal behavior of distortion product otoacoustic emissions

The temporal behavior of the 2f1-f2 distortion product otoacoustic emission is theoretically investigated for the case in which the lower frequency (f1) primary tone is on continuously, and the higher frequency (f2) one is pulsed on and off [e.g., Talmadge et al., J. Acoust. Soc. Am. 105, 275-292 (1999)]. On physical grounds, this behavior is expected to be characterized by various group delays associated with the propagation of (1) the f2 cochlear primary wave between the cochlear base and the primary distortion product generation region around x2 (the f2 tonotopic place), and (2) the 2f1-f2 cochlear distortion product (DP) waves between the cochlear base, the primary generation region of the distortion product, and the region around the 2f1-f2 tonotopic place where the generated apical moving DP wave is reflected toward the cochlear base [e.g., Talmadge et al., J. Acoust. Soc. Am. 104, 1517-1543 (1998)]. An approximate analytic expression is obtained for this behavior from the analysis of the Fourier integral representation of the auditory peripheral response to the primary stimuli. This expression also approximately describes the transient build-up of the components of different latencies in terms of the damping properties of the cochlear partition. It is shown that considerable caution must be applied in attempting to relate phase derivatives of the distortion product otoacoustic emissions for steady state stimuli and the physical time delays which are associated with the temporal behavior of a distortion product emission in the case of a pulsed primary.