Functional dissection of Neuron Network by Identification Method for Non-linear Signal Processing in Informational Engineering

本文研究了感觉神经元的功能解剖方法及其所揭示的脉冲密度编码特性。本文用非线性信号处理系统的Wiener分析方法研究了蟋蟀风敏感机械感受器神经元对高斯白色噪声刺激的锋电位串活动。从系统中提取的二阶维纳核与相应的一阶（线性）核的直积成比例。因此，该系统等效于静态非线性元件跟随线性动态元件的级联，线性动态元件的时域脉冲响应与一阶核成比例。静态非线性元件代表脉冲频率调制器，其尖峰放电的概率仅取决于其输入的瞬时幅度，即无记忆。利用Hermite多项式对放电概率与输入幅度的关系曲线进行了适当的展开。由于系统输入的高斯白色噪声的线性卷积，静态非线性元件的输入也是高斯过程。高斯权重下的厄米多项式的正交性允许确定的系数的扩展，并提供了一个曲线的尖峰放电特性的神经元。通过与一阶核的线性卷积，从系统的观察到的实际输出与估计输入的多项式值之间的内积计算系数。神经生理学特性揭示了本系统识别的方法也被描述。

A method for functional dissection of sensory neuron and pulse-density encoding properties revealed by the method are studied. Spike train activities of wind sensitive mechanoreceptor neurons in cricket, in response to a Gaussian white noise stimulus, have been studied by the Wiener's analysis as a non-linear signal processing system. The 2nd order wiener kernel extracted from the system was proportional to the direct product of corresponding 1st order (linear) kernels. The system is, therefore equivalent to the cascade of a static non-linear element following the linear dynamic element whose time-domain impulse response is proportional to the 1st order kernel. The static non-linear element represents a pulse frequency modulator whose probability of spike discharge depends solely on the instantaneous amplitude of its input, i.e. memoryless. The curve of spike firing probability as a function of input amplitude was expressed by an appropriate expansion with Hermite polynominals. The input of the static non-linear element is also a Gaussian process, because of linear convolution of the Gaussian white noise of the system input. The orthogonality of the Hermite polynominals under Gaussian weight permits the determination of the coefficients of the expansion, and provides a curve of the spike firing characteristics of the neuron. The coefficients were calculated from the inner product between the observed actual outputs of the system and the polynominal values of the estimated input by linear convolution with 1st order kernel. Neurophysiological properties revealed by the present method of system identification are also described.