4_2_09_NonlinearSystemIdentification

4_2_09_NonlinearSystemIdentification - In a black-box model...

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Unformatted text preview: In a black-box model, we try to describe a system well enough to predict its responses without knowing what is inside the system. If the black box is linear, then we can describe the system fully with the impulse response, as any stimulus is a sum of impulses. The impulse response D(t) is the reaction to a very short stimulus at time zero. One can use this model to estimate (r est (t)) the response of a linear system to stimulus s(t): r est t ( ) = r + d τ D τ ( ) s t − τ ( ) ∞ ∫ The impulse response L(t) is the reaction to a very short stimulus at time zero. One can use this model to estimate (R(t)) the response of a linear system to stimulus S(t): R t ( ) = d τ L τ ( ) S t − τ ( ) ∞ ∫ The generalization of the impulse response to nonlinear systems is the Volterra Kernel L (n) ( U 1 … U n ): V n L n ( ) , S ⎡ ⎣ ⎤ ⎦ t ( ) = d τ 1 d τ n L n ( ) τ 1 τ n ( ) ∞ ∫ ∞ ∫ S t − τ 1 ( ) S t − τ n ( ) R t ( ) = V n L n ( ) , S ⎡ ⎣ ⎤ ⎦ n = ∞ ∑ t ( ) On-Off retinal ganglion cells have no first-order kernels (B) but significant second-order ones. kernels (B) but significant second-order ones....
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4_2_09_NonlinearSystemIdentification - In a black-box model...

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