Harte James M, Elliott Stephen J, Rice Henry J
Institute of Sound and Vibration Research, University of Southampton, University Road, Southampton, Hampshire, S017 1BJ, United Kingdom.
J Acoust Soc Am. 2005 Jun;117(6):3777-86. doi: 10.1121/1.1906059.
The vibration response of the basilar membrane in the cochlea to sinusoidal excitation displays a compressive nonlinearity, conventionally described using an input-output level curve. This displays a slope of 1 dB/dB at low levels and a slope m < 1 dB/dB at higher levels. Two classes of nonlinear systems have been considered as models of this response, one class with static power-law nonlinearity and one class with level-dependent properties (using either an automatic gain control or a Van der Pol oscillator). By carefully choosing their parameters, it is shown that all models can produce level curves that are similar to those measured on the basilar membrane. The models differ, however, in their distortion properties, transient responses, and instantaneous input-output characteristics. The static nonlinearities have a single-valued instantaneous characteristic that is the same at all input levels. The level-dependent systems are multi-valued with an almost linear characteristic, for a given amplitude of excitation, whose slope varies with the excitation level. This observation suggests that historical attempts to use functional modeling (i.e., Wiener of Volterra series) may be ill founded, as these methods are unable to represent level-dependent nonlinear systems with multi-valued characteristics of this kind.
耳蜗中基底膜对正弦激励的振动响应呈现出压缩非线性，传统上用输入-输出电平曲线来描述。该曲线在低电平时斜率为1 dB/dB，在高电平时斜率m < 1 dB/dB。两类非线性系统被视为这种响应的模型，一类具有静态幂律非线性，另一类具有电平依赖特性（使用自动增益控制或范德波尔振荡器）。通过仔细选择它们的参数，结果表明所有模型都能产生与在基底膜上测量的曲线相似的电平曲线。然而，这些模型在失真特性、瞬态响应和瞬时输入-输出特性方面存在差异。静态非线性具有单值瞬时特性，在所有输入电平下都是相同的。对于给定的激励幅度，电平依赖系统是多值的，具有几乎线性的特性，其斜率随激励电平而变化。这一观察结果表明，历史上使用功能建模（即维纳或沃尔泰拉级数）的尝试可能没有充分依据，因为这些方法无法表示具有这种多值特性的电平依赖非线性系统。
