Time-delay polynomial networks and rates of approximation

[摘要] We consider a large family of finite memory causal time-invariant mapsGfrom an input setSto a set ofℝ-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 aGusing a two-stage structure consisting of a tapped delay line and a static polynomial networkN. This upper bound depends on the degree of the multivariable polynomial that characterizesN. Also given is a lower bound on the worst-case error in approximating aGusing 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.

[学科分类] 工程和技术（综合）