SEQUENTIAL ANALYSIS OF THE VISUAL EVOKED POTENTIAL SYSTEM IN MAN; NONLINEAR ANALYSIS OF A SANDWICH SYSTEM *
SEQUENTIAL ANALYSIS OF THE VISUAL EVOKED POTENTIAL SYSTEM IN MAN; NONLINEAR ANALYSIS OF A SANDWICH SYSTEM *
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人类视觉诱发电位系统的序列分析；
DOI：
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发表时间：
1980
影响因子：
5.2
通讯作者：
D. Reits
中科院分区：
文献类型：
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作者：
D. Reits
虽然线性系统只存在于理论模型中，但线性技术在物理系统分析中的应用已经很成熟。其原因是，非线性系统经常可以用近似线性的方式来研究，例如，通过使用“小”信号。在这种情况下，可以使用具有预测潜力的线性分析的全部力量。应该强调的是，“扰动”分析仅适用于系统中（平滑）非线性元件输入处较弱的信号。因此，只有当阈值"检测器"是变换链中的最后一个和唯一的非线性时，与噪声不同的恒定响应准则才满足这个条件。如果不考虑这一点，就可能对系统要素得出错误的结论。例如，假设负责闪烁感知的生理系统由以下三个连续阶段组成：（a）静态平方根（饱和）元件，（B）一阶低通线性滤波器，以及（c）阈值检测器。如果用恒定平均强度的正弦波调制光测试该系统，则对于超过线性滤波器的截止频率的刺激频率，阈值需要越来越高的调制深度。为了在线性滤波器的输出端保持恒定的幅度以增加频率，滤波器的输入幅度必须与频率成比例地增加。由于平方根元件，为了在频率加倍的情况下在滤波器的输入处获得振幅的加倍，刺激振幅必须四倍。这导致高频衰减是实际存在的两倍。因此，恒定响应分析表明二阶低通滤波器后面跟着阈值检测器。这个错误的结论本可以避免，因为只有当除了幅度之外，响应的所有其他方面（如延迟、波形等）都保持恒定时，恒定响应方法才适用!这些限制在心理物理学中经常被忽视。当考虑到系统的非线性方面时，输入输出分析的结果根据定义几乎没有预测价值。由于叠加原理只适用于线性系统，非线性系统的输入输出关系的知识只对实际激励有效。有人可能会说，对于可以展开为沃尔泰拉级数的非线性系统，情况并非如此。然而，对于一个完整的描述，这样的系统的所有维纳内核必须确定。这不是一个现实的提议。一般来说，非线性系统的完整描述是不可行的;输入信号的类别总是受到限制，并且所有
Although linear systems exist only in theoretical models, the application of linear techniques in the analysis of physical systems is well established. The reason for this is that nonlinear systems can frequently be investigated in such a way that their behavior is approximately linear, for example, by using “small” signals. In that situation the full power of a linear analysis with its predictive potential can be employed. It should be emphasized that a “perturbation” analysis holds only for signals that are weak at the input of the (smooth) nonlinear elements in a system. Therefore, a constant response criterion, just differing from noise, fulfills this condition only if the threshold “detector” is the last and sole nonlinearity in the chain of transformations. Without this consideration, erroneous conclusions can be reached about the system elements. Suppose, for example, that the physiological system responsible for flicker perception consists of the following three sequential stages: (a) a static square root (saturating) element, (b) a first-order, low-pass linear filter, and (c) a threshold detector. If this system is tested with a sine-wave-modulated light of constant mean intensity, then for stimulus frequencies exceeding the cut-off frequency of the linear filter, increasingly higher modulation depths are required for threshold. To maintain a constant amplitude at the output of the linear filter for increasing frequencies, the input amplitude of the filter must increase proportionally to frequency. Because of the square root element, to obtain a doubling of amplitude a t the input of the filter with a doubling of frequency, the stimulus amplitude must quadruple. This results in a high-frequency attenuation that is twice as steep as that actually present. Thus, a constant response analysis indicates a second-order low-pass filter followed by a threshold detector. This erroneous conclusion could have been avoided with the consideration that a constant response approach is applicable only if, in addition to amplitude, all other aspects of the response, like latency, waveform, and so forth, are kept constant! These restrictions are frequently ignored in psychophysics. When nonlinear aspects of a system are taken into account, the results of an inputboutput analysis have by definition little predictive value. As the superposition principle holds only for linear systems, knowledge of the inputboutput relation of a nonlinear system is only valid for the actual stimulus employed. One may argue that this is not the case for a nonlinear system that can be expanded in a Volterra series.’,* However, for a complete description all Wiener kernels of such a system must be determined. This is not a realistic proposition. In general, a complete description of a nonlinear system is not feasible; the class of input signals is always restricted and all