Practical nonlinear system analysis by Wiener kernel estimation in the frequency domain
Practical nonlinear system analysis by Wiener kernel estimation in the frequency domain
复制标题
通过频域维纳核估计进行实用非线性系统分析
DOI：
10.1007/bf00360650
复制
发表时间：
1976
影响因子：
1.9
通讯作者：
A. S. French
中科院分区：
文献类型：
--
作者：
A. S. French
具有有限记忆和时不变的非线性系统可以用维纳泛函展开完全描述，其中一系列多维核提供了非线性行为的多项式近似。这些核在最小均方意义上给出了对整个系统行为的最佳拟合估计，因此可以用于描述非线性包括不连续函数的系统。由Lee和Schetzen描述的维纳方法的一种修改，它使用根据相互关联函数定义的核，已经在分析非线性系统的大多数实际尝试中使用，但是我们之前已经描述了如何用频域的复乘法代替相互关联。快速傅里叶变换提供的域转换速度使该方法比时域估计更有效。本文描述了该技术在中型数字计算机上对输出为连续或脉冲信号的非线性系统的实际实现。这个描述应该足以让其他人实现分析方案。该技术非常适合分析非线性生物系统，特别是在神经生理学中遇到的非线性系统，因为它的通用性，处理硬非线性的能力以及易于使用具有脉动输出的系统。
Nonlinear systems which have finite memories and are time invariant can be completely described by the Wiener functional expansion, in which a series of multidimensional kernels provide a polynomial approximation to the nonlinear behaviour. The kernels give a best fitting estimation to the total system behaviour in the least mean square sense and can therefore be used to describe systems in which the nonlinearities include discontinuous functions. A modification of the Wiener method described by Lee and Schetzen, which uses kernels defined in terms of cross correlation functions, has been used in most practical attempts to analyse nonlinear systems, but we have previously described how the cross correlations may be replaced with complex multiplications in the frequency domain. The speed of domain translation offered by the fast Fourier transform makes this method more efficient than time domain estimation. In this paper the practical implementation of the technique on a medium sized digital computer is described for nonlinear systems whose outputs are continuous or pulsatile signals. This description should be adequate to allow others to implement the analysis scheme. The technique is well suited to the analysis of nonlinear biological systems, particularly those encountered in neurophysiology, because of its generality, ability to deal with hard nonlinearities and ease of use with systems having pulsatile outputs.