TY - JOUR
T1 - Identification of nonlinear systems using random amplitude poisson distributed input functions
AU - Wu, Yu Te
AU - Sclabassi, Robert J.
N1 - Funding Information:
Manuscript received December 22, 1993; revised July 22, 1995 and May 11, 1996. This work was supported by NIMH under Grant MH00343, ONR under Grant N000147-87-K-0472, and AFOSR under Grant 89-1097. The authors are with the Laboratory for Computational Neuroscience, Departments of Neurological Surgery and Electrical Engineering, University of Pittsburgh, Pittsburgh, PA 15213 USA (e-mail: [email protected]). Publisher Item Identifier S 1083-4427(97)00129-X.
PY - 1997
Y1 - 1997
N2 - In this paper, nonlinear system identification using a doubly random input function which is a Poisson train of events with random amplitudes as a system input is investigated. These doubly random input functions are useful for identifying systems that naturally require amplitude modulated point process inputs as stimuli such as the hippocampal formation in the central neurous system. This is an extension of earlier work in which a Poisson train of events with only constant amplitude was used as the input for system identification. Analogous to the Wiener theory, we have developed both continuous and discrete functionals up to second-order for this doubly random input function. Closed form solutions for the diagonal terms of the second-order kernels in both cases have been obtained and convergence properties are demonstrated. Two hypothetical discrete second-order nonlinear systems are illustrated and one of them was simulated to test the theory presented. Discrete kernels computed from the simulated data agree with the theoretical prediction.
AB - In this paper, nonlinear system identification using a doubly random input function which is a Poisson train of events with random amplitudes as a system input is investigated. These doubly random input functions are useful for identifying systems that naturally require amplitude modulated point process inputs as stimuli such as the hippocampal formation in the central neurous system. This is an extension of earlier work in which a Poisson train of events with only constant amplitude was used as the input for system identification. Analogous to the Wiener theory, we have developed both continuous and discrete functionals up to second-order for this doubly random input function. Closed form solutions for the diagonal terms of the second-order kernels in both cases have been obtained and convergence properties are demonstrated. Two hypothetical discrete second-order nonlinear systems are illustrated and one of them was simulated to test the theory presented. Discrete kernels computed from the simulated data agree with the theoretical prediction.
UR - http://www.scopus.com/inward/record.url?scp=0031104418&partnerID=8YFLogxK
U2 - 10.1109/3468.554684
DO - 10.1109/3468.554684
M3 - Article
AN - SCOPUS:0031104418
SN - 1083-4427
VL - 27
SP - 222
EP - 234
JO - IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans.
JF - IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans.
IS - 2
ER -