Interpretation Of Wiener Kernels

Abstract

We have studied the Wiener kernels of simulated nonlinear systems to lend insight into the interpretation of these kernels. Using Wiener kernels gives as much information as possible in the lower order kernels. We have seen that using high power inputs gives a good global description of the non linearities of the system. It does not necessarily give an accurate description. By using smaller input power and a variety of DC bias levels, it is possible to study the nonlinearities in a number of local regions to get a better description of the nonlinearities. Thus the paradigm use of the kernel identification approach would be, first, to identify with a large power input signal, then to study regions of particular interest with smaller input signals. By decomposing the model of the pupil system into subsystems, we can see the cause for certain anomalous behavior in the kernels. The pupil tends to hide many of its interesting properties with the slow dynamics of the iris musculature. Only by examining the kernels closely can one find the more interesting nonlinearities which arise in the system. The second order kernels of the pupil systems demonstrates that the memory in the system is largely after the nonlinearities. But careful inspection leads us to the conclusion that some memory also appears before the nonlinearity, and that this memory in dependent on input power level and DC bias. This exercise makes it clear that one kernel cannot elucidate all of the information available about a system. Rather, an army of kernels may be necessary to describe the local and global behaviors of a system. 0..