## Complex Signal Processing using Non-Linear Auditory Frequency Selectivity

### L. P. O'Mard, E. A. Lopez-Poveda & R. Meddis

#### Abstract

We present a phenomenological filter model that simulates the non-linear characteristics of basilar membrane filtering in mammalian cochlea. Preliminary results from a full auditory nerve model are also presented. Cochlear non-linearity has already been shown to have important functions in the processing of complex stimuli by mammals. The Dual Resonance Non-linearity (DRNL) filter model closely simulates empirical results obtained from mechanical cochlear experiments. This purely passive model demonstrates a centre-frequency shift, and filter width increase with a rise in stimulus level. It also reproduces two-tone suppression, distortion products and other data dependent upon cochlear non-linearity. The DRNL model is a composite filter consisting of two parallel filter paths: one linear and the other containing a compressive non-linearity. The model parameters were optimised at best frequencies of 0.3, 8 and 18 kHz, using simulated annealing. The model was incorporated into an auditory simulation computing library (LUTEar) and used to demonstrate non-linear auditory phenomena.

#### Introduction-Why Non-Linearity is Important

The majority of naturally occuring sound stimuli are complex. Stimuli such as speech contain many frequency components. In a non-linear system these different components interact. Cochlear non-linearity also serves to map a huge dynamic range of physical stimuli into the limited dynamic range of nerve firings. For example, humans can perceive the change in stimulus intensity from 20 to 22 dB SPL just as well as from 90 to 92 dB SPL. The importance of non-linearity in cochlear processing has been covered by many studies in recent years. Results have been presented linking the non-linearity to an apparent enhancement of the representation of speech sounds in broad band noise (Deng and Geisler, 1987). It is known that distortion products influence pitch perception-the so-called second effect of pitch shift (Schouten et al., 1962)-and pitch is an important element in the segregation of sounds. It has also been shown that the non-linear response of the cochlea has important implications for the representation of speech sounds , i.e., actual multi-channel auditory nerve recordings do not resemble linear filter outputs (Miller and Sachs, 1983).

#### Dual Resonance Non-Linear (DRNL) Model Schematic

The DRNL filter contains five basic elements: three gamma tone filters a (Butterworth) low-pass filter and a compressive non-linearity. The DRNL filter-elements are grouped into two parallel filter paths, one sensitive and sharply tuned-designated as the narrow filter path, and the other less sensitive and broadly tuned-the wide filter path. There is no feedback loop in the DRNL filter, so the model is inherently stable |

#### Fitting the DRNL Model to Mechanical Data

Extensive mechanical measurements are only available from restricted points on the first, third and fourth turns of the cochlea, around the 0.3, 8 and 18 kHz BF regions. The figure shows a comparison between the scaled model response and BM data at 8 kHz (Rhode et. al, 1986).

The model parameters were optimised using simulated annealing (Kirkpatrick et al., 1983).

#### Auditory Nerve Model

##

- Pre-emphasis (Outer-/Middle ear) filtering using a 2nd order band pass filter.
- DRNL Basilar Membrane filter model.
- Inner hair-cell receptor potential model (Shamma et al, 1986).
- Inner hair-cell synapse model (Meddis, 1986) with an exponential permeability function (Sewell, 1984).
- DRNL Intensity-Dependent Characteristics

#### DRNL Intensity-Dependent Characteristics

Johnstone et al. (1986) showed how the BM response becomes more broadly tuned and peaks at lower frequencies as stimulus intensity is raised. Broadening occurs as the wide filter path contribution to the model output increases, relative to that of the narrow filter path -the narrow filter path response is subject to compression at high signal levels.

The lower BF at higher intensities is also caused by the wide filter path response overwhelming the narrow path response. The wide filter path has a lower centre frequency.

#### Distortion Products

DPs can be seen in auditory nerve responses, and this fact provided some of the strongest evidence for cochlear non-linearity. Recent measurements have now shown that DPs are present in the mechanical response of the BM. Tones f1 (36 kHz) and f2 (38 kHz) were presented simultaneously to the filter, set at 34 kHz BF (CDT=2f1-f2). The intensity of f2 was varied while the level of f1 was held at 81 dB SPL. The filter output was then Fourier transformed, and the level of the primary and the CDT components were determined. |

#### Rate-Intensity Functions

| The non-linear response of the DRNL filter allows us to produce better low, medium and high spontaneous rate auditory nerve (AN)fibre responses(Sachs and Abbas, 1974). The figure shows model and experimental fibre responses at 18 kHz BF. The comprehensive AN data available will enable us to further refine the DRNL model parameters at points not accessible to mechanical measurement.

#### Cochleagrams

Linear filterbank | Non-linear filterbank

Non-linear transformations of acoustic stimuli may give rise to a more useful representation of signals. Secker-Walker and Searle (1990) showed that such representations were visibly easier to use when estimating formant frequencies in terms of the formant period.

The figures clearly show an enhancement of pitch- and formant-related detail in the time domain when the non-linear filter-bank is used.

Although the filter was only optimised at three points, a crude filter-bank was produced by extrapolating between the optimised filter parameters as a function of BF.

#### Two-Tone Suppression-Auditory Nerve

| A 28 dB SPL probe tone was played continuously at BF (8 kHz), while a test tone was varied in frequency and intensity. The different shadings in the the graphs represent the output intensity responses evoked by the test stimulus. The blue regions on the graphs show areas of suppression and the red, excitatory regions. The yellow circle indicates the position of the probe tone.

The below-BF suppresion region is shallower than the region above-BF. It disappears if the probe tone intensity is increased. The above-BF region has very deep levels of suppresion which remain for very high probe tone intensities.

#### Summary and Conclusions

We have presented a computational non-linear filter-bank model of the BM. The DRNL model was designed to account for observed BM phenomena, without detailed concern for biophysical mechanism. The model has been compared against an extensive range of experimental data, which it has replicated qualitatively and in most cases quantitatively. In particular, the model produces non-linear effects such as two-tone suppression, distortion products and other intensity dependent phenomena-such as increasing bandwidth and lower BF. The model has also shown that it is possible to reproduce realistic non-linear BM behaviour without the need for an active gain control mechanism.

The model consists of digital filters, which accept the arbitrary wave forms typical of the stimuli used by auditory investigators. A filter-bank was produced by extrapolating between the optimised filter parameters at each BF. The filter-bank has been incorporated into the LUTEar computer library which is widely available.

An auditory nerve model, using the DRNL has been produced. Work is in progress to further refine the DRNL model with the use of the wider range of auditory nerve data which is available.

#### References

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- Cooper N. P. and Rhode W. S. (1995) "Nonlinear mechanics at the apex of the guinea-pig cochlea" Hearing Research 82, 225-243.
- Deng L. and Geisler C. D. (1987) "A composite auditory model for processing speech sounds" JASA. 82, 2001-2012.
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- LUTEar (1993): This is a flexible computing tool for auditory simulation. It runs on all the major platforms, and is available over the internet via anonymous FTP.
- Miller M. I and Sachs M. B. (1983) "Representation of stop consonants in the discharge patterns of auditory nerve fibres" JASA., 74, 502-517.
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