Accession Number:

ADA175130

Title:

Fading Memory and the Problem of Approximating Nonlinear Operators with Volterra Series,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV BERKELEY DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES

Personal Author(s):

Report Date:

1985-11-01

Pagination or Media Count:

12.0

Abstract:

Using the notion of fading memory we prove very strong versions of two folk theorems. The first is that any time-invariant TI continuous nonlinear operator can be approximately by a Volterra series operator, and the second is that the approximating operator can be realized as a finite- dimensional linear dynamical system with a nonlinear readout map. While previous approximation results are valid over finite time intervals and for signals in compact sets, the approximations presented here hold for all time and for signals in useful noncompact sets. The discrete-time analog of the second theorem asserts that any TI operator with fading memory can be approximated in our strong sense by a nonlinear moving-average operator. Some further discussion of the notion of fading memory is given. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE