FIGURE 8.3-10 (A) Canonical structure of a nonlinear system having two independent, uncorrelated noise inputs. The F12, 2I/SO system allows mixing of the two inputs. (B) Wiener system approximating the 2I/SO nonlinear system. Only the first two kernels and the second-order cross kernel are used. See text for comments.

is used on what is basically a nonlinear system, different input stimulus noise conditions can give different results.

The Lee-Schetzen-Marmarelis white noise method described in Section 8.3 is more general and powerful than the TCA. The white noise method gives a very abstract description of a neuro-sensory system that is characterized by kernels or weighting functions. The first-order kernel is basically the weighting function of the neuro-sensory system if it is purely linear, the same result as x+(x) from the TCA. If the neuro-sensory system is nonlinear (and it always is), the white noise method also gives higher-order kernels or system weighting functions corresponding to the nonlinear behavior. A major problem seen with the white noise method is that kernels of order 3 or higher, which are necessary to describe a very nonlinear system, have more than three dimensions, and cannot easily be visualized or interpreted. The second-order kernel however, h2(x1, t2), is a three-dimensional function that is usually visualized as a two-dimensional contour plot.

The white noise method has been applied successfully to retinal systems and to spinal motoneurons. The white noise method yields a black-box description of the neuro-sensory system being studied. The usefulness of this type of model is enhanced if it can be correlated with neuron structure and interconnections.

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