From Hearing to Listening: Design and Properties of an Actively Tunable Electronic Hearing Sensor

Abstract

An important step towards understanding the working principles of the mammalian hearing sensor is the concept of an active cochlear amplifier. Theoretical arguments and physiological measurements suggest that the active cochlear amplifiers originate from systems close to a Hopf bifurcation. Efforts to model the mammalian hearing sensor on these grounds have, however, either had problems in reproducing sufficiently close essential aspects of the biological example (Magnasco, M.O. Phys. Rev. Lett. 90, 058101 (2003); Duke, T. & Jülicher, F. Phys. Rev. Lett. 90, 158101 (2003)), or required complicated spatially coupled differential equation systems that are unfeasible for transient signals (Kern, A. & Stoop, R. Phys. Rev. Lett. 91, 128101 (2003)). Here, we demonstrate a simple system of electronically coupled Hopf amplifiers that not only leads to the desired biological response behavior, but also has real-time capacity. The obtained electronic Hopf cochlea shares all salient signal processing features exhibited by the mammalian cochlea and thus provides a simple and efficient design of an artificial mammalian hearing sensor.

Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

“…By substituting these signals in (1), this particular feature enables the calculation of algebraic Equations [3][4][5] that describe the input-output amplitude relation ( ) (4) as well as the phase relation The stimulation strength, starting at 1 0 = a with the upper curve, is decreased in steps of 10 dB. The input-output behavior shows a strong amplification of faint input signals with a sharper resonance for a smaller distance to the bifurcation point.…”

“…The input-output behavior shows a strong amplification of faint input signals with a sharper resonance for a smaller distance to the bifurcation point. This is one of the main effects a cochlea model has to exhibit [1][2][3][4][5][6][7]. In resonance ) ( …”

“…Despite the nonlinearity of the so called Hopf-type amplifier, the study of the response characteristic has exposed, that a sinusoidal input signal leads to a pure sinusoidal output signal with the same frequency and without any harmonic distortions [3][4][5][6][7][8][9]. That means, apart from the specific nonlinear amplification characteristic, this Hopf-type amplifier acts on single-tone excitations like a linear system concerning the spectral behavior [8,9].…”

“…To describe these biological features, the (truncated) normal form equation of the Andronov-Hopf bifurcation endowed with an excitation was proposed [3] and is widely used as basis element for several models of the auditory system [4][5][6][7]. To achieve the nonlinear amplification characteristic, the Hopf system is tuned close to the onset of the self-sustained limit cycle oscillation [3,4].…”

Discretization analysis of bifurcation based nonlinear amplifiers

“…This amplification characteristic can be modeled by a system near the onset of an Andronov-Hopf bifurcation (Eguíluz et al, 2000). Regarding this bifurcation based amplifier and after first analog realizations by Stoop et al (2005Stoop et al ( , 2007 a discrete-time system was developed and implemented on a digital signal processor (DSP) (Reit et al, 2012). This implementation was latterly improved and extended to compare nonlinear amplifiers based on Andronov-Hopf and Neimark-Sacker bifurcations (Feldkord et al, 2016).…”