Identification of nonlinear systems using random impulse train inputs
Tóm tắt
Nonlinear systems that require discrete inputs can be characterized by using random impulse train (Poisson process) inputs. The method is analagous to the Wiener method for continuous input systems, where Gaussian white-noise is the input. In place of the Wiener functional expansion for the output of a continuous input system, a new series for discrete input systems is created by making certain restrictions on the integrals in a Volterra series. The kernels in the new series differ from the Wiener kernels, but also serve to identify a system and are simpler to compute. For systems whose impulse responses vary in amplitude but maintain a similar shape, one argument may be held fixed in each kernel. This simplifies the identification problem. As a test of the theory presented, the output of a hypothetical second order nonlinear system in response to a random impulse train stimulus was computer simulated. Kernels calculated from the simulated data agreed with theoretical predictions. The Poisson impulse train method is applicable to any system whose input can be delivered in discrete pulses. It is particularly suited to neuronal synaptic systems when the pattern of input nerve impulses can be made random.
Tài liệu tham khảo
Brillinger, D.R.: The identification of polynomial systems by means of higher order spectra. J. Sound Vib.12, 301–313 (1970)
Friesen, W.O.: Physiology of the spiny lobster cardiac ganglion. Doctoral Thesis, San Diego, University of California 1974
French, A.S., Butz, E.G.: The use of Walsh functions in the Wiener analysis of nonlinear systems, IEEE Trans. Comput. C-23, 225–231 (1974)
French, A.S., Butz, E.G.: Measuring the Wiener kernels of a nonlinear system using the fast Fourier algorithm. Int. J. Control17, 529–539 (1973)
Hida, T., Ikeda, N.: Analysis on Hilbert space with reproducing kernel arising from multiple Wiener integral Proc. 5th Berkeley Symp. on Math. Stat. and Prob. Vol. II part I 117–143
Hida, T.: Stationary stochastic processes. Princeton: Princeton Univ. Press and Univ. of Tokyo Press. 1970
Lee, Y.W., Schetzen, M.: Measurement of the Wiener kernels of a nonlinear system by cross-correlation. Int. J. Control2, 237–254 (1965)
Marmarelis, P.Z.: Nonlinear dynamic transfer functions for certain retinal neuronal systems. Doctoral Thesis, California Institute of Technology 1971
Marmarelis, P.Z., Naka, K.-I.: White-noise analysis of a neuron chain: An application of the Wiener theory. Science175, 1276–1278 (1972)
Marmarelis, P.Z., McCann, G.D.: Development and application of white-noise modeling techniques for studies of insect visual nervous system. Kybernetik12, 74–89 (1973)
Marmarelis, P.Z., Naka, K.-I.: Nonlinear analysis and synthesis of receptive-field responses in the catfish retina. I: Horizontal cell chain. J. Neurophysiol.36, 605–618 (1973)
Marmarelis, P.Z., Naka, K.-I.: Nonlinear analysis and synthesis of receptive field responses in the catfish retina. II: One-input white-noise analysis. J. Neurophysiol.36, 619–633 (1973)
Marmarelis, P.Z., Naka, K.-I.: Nonlinear analysis and synthesis of receptive field responses in the catfish retina. III: Two-input white-noise analysis. J. Neurophysiol.36, 634–648 (1973)
Marmarelis, P.Z., Naka, K.-I.: Identification of multi-input biological systems. IEEE Transactions on Biomedical Engineering, Vol. BME-21 No.2, 88–101 (1974)
McShane, E.J.: Stochastic integrals and non-linear processes. J. Math. Mech.11, 235–283 (1962)
Ogura, Hisanao: Orthogonal Functionals of the Poisson Process. IEEE Trans. Inform. Theory. IT-18 No. 4, 473–481 (1972)
Picton, T.W., Hillyard, S.A., Krausz, H.I., Galambos, R.: Human auditory evoked potentials. I: Evaluation of components. Electroenceph. clin. Neurophysiol.36, 179–190 (1974)
Rothman, H.H., Davis, H., Hay, I.S.: Slow evoked cortical potentials and temporal features of stimulation. Electroenceph. clin. Neurophysiol.29, 225–232 (1970)
Stark, L.: Neurological control systems, studies in bioengineering, Ch. 4. New York: Plenum Press 1968
Volterra, V.: Theory of functionals and of integral and integro-differential equations. New York: Dover Publications. 1959
Wiener, N.: Nonlinear problems in random theory. New York: Wiley 1958