PHASE BEHAVIOR OF THE PRIMARIES IN DISTORTION PRODUCT ANALYSIS A. VETEŠNÍK Department of Theoretical Physics, Palacký University, Svobody 26, 77146 Olomouc, Czech Republic E-mail: a.vetesnikqseznam.ch R. NOBILI Dipartimento di Fisica ''G.Galilei'', Università di Padova, via Marzolo 8, 35131 Padova, Italy E-mail:
[email protected] Current analysis of nonlinear distortion phenomena is often based on the perturbation approximation assumption that the response of the basilar membrane (BM) to a pair of input tones is a simple superposition of the responses to the tones as if they were separately inputted [1]. Moreover, the estimate of the phase delays between the distortion product (DP) responses on the BM and those detected as frequency components of otoacoustic emissions are based on the concept that the cochlear partition behaves as a transmission line. Frequency-domain simulations based on a nonlinear hydrodynamic model of the human cochlea [2,3] lead to results that contrast both such beliefs.
Introduction Frequency-domain simulations of distortion product (DP) generation and nonlinear interaction amongst traveling waves are here sampled. Simulations were carried out on a hydrodynamic model of the cochlea in which the main physical and geometric parameters of the human cochlea were represented. The relevant features of the model are: tectorial membrane weakly resonating at the characteristic frequency (CF) of the BM; viscous BM-outer hair cell coupling provided by the Deiters’ cells; saturation of the cochlear amplifier at ~35 dB sound pressure level; smooth cochlear amplifier gain with maximum 50-55 dB amplification in the 1-3 kHz range. Results Our simulations show that the main source of the distortion product is not the CF site of f2, as hypothesized in [1], but the site of the f2 amplitude fall. Also, the phase behaviors of the primaries and the cubic DPs appear discrepant with those usually assumed in current literature. The discrepancies became relevant as the input levels approach the input/output curve plateaux from below. A striking feature of our simulations is the total agreement of the DP emission amplitudes as functions of f2/f1 ratio with experimental data from humans.
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Figure 1. BM displacements elicited by two tones (primary frequencies) of equal level resolved into their main frequency components, i.e. the primaries (dot- and dash-dot line) and the distortion product (DP) 2f1-f2 (A,B) and 2f2-f1 (C,D), (DP, solid line), as a function of fractional distance from stapes. (A,C: amplitudes; B, D: phases). Note the remarkable distortion of the phase profile affecting the DP at its generation site. The segment S in A shows the region where the DP phase is very close to the 2φ1-φ2, i.e. the DP phase as in the first order perturbation approximation.
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References 1. Knight, R.D., Kemp, D.T., 2001. Wave and place fixed DPOAE maps of the human ear. J. Acoust. Soc. Am. 109, 1513-1525. 2. Nobili, R., Mammano, F., Ashmore, J., 1998. How well do we understand the cochlea? Trends Neurosci. 21, 159-167. 3. Harris, F.P., Lonsbury-Martin, B.L., Stagner, B.B., Coats, A.C., Martin, G.K., 1989. Acoustic distortion products in humans: systematic changes in amplitudes as a function of f2/f1 ratio. J. Acoust. Soc. Am. 85, 220-229.
