Time-frequency distributions of click-evoked otoacoustic emissions
Introduction
The waveform of a transiently evoked otoacoustic emission (TEOAE) typically depends on the spectral energy of the stimulus, the number and tuning of the emission generators located within the organ of Corti, and on the middle ear transmission characteristics. When a broad-band stimulus is used, the corresponding response shows the presence of several dominant frequencies with different onset times and damping, resulting in an OAE with a complex waveform. In contrast, tone bursts or other frequency-specific stimuli evoke a modulated emission at about the same frequency of the stimulus (Wit et al., 1981; Zwicker and Schloth, 1984; Bonfils and Uziel, 1989; Grandori, 1985; Grandori and Antonelli, 1986).
The time of appearance of a component seen in a TEOAE is intimately related to the frequency of the component itself, i.e., the higher the frequency the shorter the latency, and vice versa, the lower the frequency the longer the latency. It is well known, on the other hand, that emissions evoked by broad-band stimuli, such as clicks, show a ‘frequency dispersion’ reminiscent of the place-frequency distribution along the cochlea (Kemp, 1979; Wit and Ritsma, 1980; Wit et al., 1994a). Analysis of the time-frequency properties of TEOAEs is therefore of considerable interest due to their close relation with cochlear mechanisms. In particular, since OAEs in response to click stimuli evoke a cumulative response from the whole cochlea, the analysis of click-evoked OAEs can yield a global view of cochlear function.
Measurements of time-frequency properties of TEOAEs have encountered a variety of technical problems such as the difficulty in determining the contribution of each single elementary frequency component of such a complex response. The traditional Fourier transform is not suitable for the description of transient signals (such as TEOAEs) since it gives no information on frequency changes along with time. On the other hand, by means of the short time Fourier transform (STFT, i.e., the Fourier transform of small consecutive segments of the signal) it is possible to obtain time-frequency distributions of transient signals, but this method suffers from poor resolution. Recently, the wavelet transform (WT) (Mallat, 1989; Daubechies, 1990) has been successfully used to derive time-frequency distributions from time-varying signals. Basically, the main difference between the STFT and the WT is that the resolution of the WT is not fixed over the entire time-frequency plane but can vary. In this way, high-frequency components can be analyzed with a good time resolution while low-frequency components can be analyzed with a good frequency resolution.
Time-frequency distributions of OAEs were recently derived by means of the Wigner, the Choi-Williams, and the pseudo-Wigner-Ville distributions (Cheng, 1995; Kollmeier and Uppenkamp, 1989; Özdamar, personal communication), and by filter banks (Pasanen et al., 1994). Analysis of TEOAEs by means of wavelets has been previously presented by Wit et al. (1994a). They showed that wavelets are well suited for the analysis of TEOAEs and that the wavelet approach was able to produce accurate information on the time-frequency properties of the recorded emission. In particular, in the above-mentioned study the WT has been used as a tool to compare the time-frequency properties of real OAEs and OAEs synthesized by computer.
In our study we have used the family of wavelets proposed by Wit et al. (1994a)to further investigate the reliability of the WT for the description of time-frequency properties of click-evoked OAEs. We propose here a new technique (based on the inverse WT) to decompose emissions into elementary components. The temporal evolution of the elementary components will be described in some detail and a measure of their latencies will be defined and derived.
Section snippets
Materials and methods
Eight subjects, aged 20–35 years, participated in the study. All were in good general health and had no previous history of ear disease.
Measurements were done in a sound-proof cabin with the subject seated in an armchair during the recording session, which lasted for about 20 min. TEOAEs were recorded using an Otodynamic ILO88 system. A standard adult probe was used. Clicks were delivered unilaterally at 8 intensities (from 47 to 68 dB SPL in 3 dB steps). Responses were filtered with the ILO88
Results
As an introductory example of the present method of wavelet analysis, we have considered a simulated signal (Fig. 1) obtained by the sum of 5 gammatones with central frequencies 1.0, 1.5, 2.2, 3.3, and 5.0 kHz (for the analytical expression of a gammatone and the special choice for the 5 gammatones frequencies, see Appendix A). Fig. 2 shows the time-frequency representation of the simulated signal. Each gammatone gives rise to a ‘hill’ in the 3-D time-frequency representation (Fig. 2, top). The
Discussion
Wavelet transform (WT) is proposed here to derive time-frequency distributions from click-evoked OAEs of normal ears. This technique is shown to be a tool to analyze the ‘frequency dispersion’ along with time. By means of a new technique, based on the inverse WT, the emission response is decomposed into elementary components whose temporal evolution has been analyzed. The elementary components are obtained by the convolution of a set of bandpass filters (i.e., the wavelets) with the OAE
Acknowledgements
Mark E. Lutman and Bert van Zanten are gratefully acknowledged for their comments on an earlier version of the manuscript. This study was partially financed by a project from the Biomedical and Health Research Programme (AHEAD, contract #PL951636).
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