Time-delay polynomial networks and rates of approximation
We consider a large family of finite memory causal time-invariant maps G from an input set S to a set of ℝ-valued functions, with the members of both sets of functions defined on the nonnegative integers, and we give an upper bound on the error in approximating a G using a two-stage structure consi...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1998-01-01
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| Series: | Mathematical Problems in Engineering |
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| Online Access: | http://dx.doi.org/10.1155/S1024123X98000726 |
| Summary: | We consider a large family of finite memory causal time-invariant maps G from an input set S to a set of
ℝ-valued functions, with the members of both sets of functions defined on the nonnegative integers, and we give an upper bound on the error in approximating a G using a two-stage structure consisting of a tapped delay line and a static polynomial network N . This upper bound depends on the degree of the multivariable polynomial that characterizes N. Also given is a lower bound on the worst-case error in approximating a G using polynomials of a fixed maximum degree. These upper and lower bounds differ only by a multiplicative constant. We also give a corresponding result for the approximation of not-necessarily-causal input–output maps with inputs and outputs that may depend on more than one variable. This result is of interest, for example, in connection with image processing. |
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| ISSN: | 1024-123X 1563-5147 |