ELSEVIER Hearing Research 81 (1994) 208-214 Qn the shape of (evoked) otoacoustic emission spectra Hero P. Wit a, * , Pim van Dijk a, Paul Avan b a zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Institute of Audiology, University Hospital, P. 0. Box 30.001, 9700 RB Groningen, the Netherlands b Biophysics Laboratory, Faculty of Medicine, Clermont-Ferrand, France Received 16 May 1994; revised 22 September 1994; accepted 30 September 1994 zyxwvutsrqponmlkjihgfedcbaZYXW Abstract In a preceding paper [Wit et al., (1994) Hear. Res. 73, 141-1471 it was shown that realistic time-frequency plots for click evoked otoacoustic emissions can be synthesized by adding a large number of gammatones. It is necessary in such a synthesis to make the inner ear frequency to place map, from which the central frequencies of the gammatones are taken, slightly irregular along the entire cochlear partition. The present paper shows that this approach leads, in a rather straightforward way, to (quasi-) periodicity in synthesized spectra of evoked otoacoustic emissions. These spectra show good resemblance with spectra from real ear emission measurements. Keywords: Otoacoustic emissions; Periodicity; Irregularity; Convolution 1. Introduction A simple straightforward (but incomplete) model for the inner ear is a bank of bandpass filters. (e.g. Patter- son et al., 1992). In a preceding paper (Wit et al., 1994) we have shown that the sum of impulse responses of the individual filters in such a filter bank can describe properties of click evoked otoqcoustic emissions. A necessary condition to obtain realistic results with such a description is that (small) randomly distributed irreg- ularities are introduced in the array of filter central frequencies. Or, in other words, that the frequency to place organization of the inner ear is chosen not to be perfect. In this paper we will show that the same, relatively simple, concept is able to generate (quasi-) periodicity in the frequency domain, despite the fact that at first sight regularity seems to be destroyed by the introduction of the above mentioned irregularities. Such periodicity is one of the characteristic features of otoacoustic emission spectra, and is most probably related to periodicity in normal hearing thresholds (Kemp, 1979; Schloth, 1983; Horst et al., 1993; Zwicker and Schloth, 1984; Long and Tubis, 1988). Our work was inspired by Shera and Zweig (1993, * Corresponding author. Fax: + 31 (SO) 696-726. 0378-5955/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0378-5955(94)00163-4 19941, who introduced random irregularities in cochlear mechanics as a very promising concept to explain prop- erties of otoacoustic emissions (e.g. Talmadge and Tubis, 1993). It is interesting to note that Gold, the predictor of (spontaneous) otoacoustic emissions, stated a few years ago that individual fibers in the inner ear would all cancel their outputs, if they were neatly overlapping (Gold, 1988), and that inaccuracies in the system are necessary to produce evoked sound. This idea is not new: already more than 10 years ago Sutton and Wilson (1983) proposed a model in which emis- sions were caused by irregularities in cochlear fre- quency mapping. The essential difference, however, between their model and the description given in this paper is that in Sutton and Wilson’s model a few localized irregularities are present, while we suppose that small random irregularities are present all along the cochlear partition. 2. Theory Consider an array of linear bandpass filters with different central frequency, arranged along an x-axis, where x is a (monotonic) function of frequency. The position of an individual filter will be denoted by xk, as shown in Fig. 1. Let z(x,,cu;x) be the (complex) filter