SEQUENTIAL ANALYSIS OF THE VISUAL EVOKED POTENTIAL SYSTEM IN MAN; NONLINEAR ANALYSIS OF A SANDWICH SYSTEM *

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