New set of signals providing kidas best interpolation approximation of band-limited signals
説明
Suppose that e(x) = f(x) -g(x) and Z(x) = f(x) -G(x) are the approximation error for the both approximations, respectively. Since the error Z(x) = f(x) - G(x) depends on the signal f(x), we express the error as 2(x) = qf(x)], Let P[2(x)] be any function/functional/operator of C(x) and let p[Z(x)] have non-negative value. We use similar notation p[e(x)] for e(x) also. Further, let 0 be a subset in Z. Then, consider the following measure of error &(x) = sup,,,{/3[6(x)]} for f = f(x) in 0. With respect to E@(x), it is natural to assume that Ee,(x) < Ee(x) holds for all t,he set of signals 0, satisfying 0, 2 0. Let Ze be the set of all the e(x)'s, where e(x) = f(x) - g(x). Then, we assume that the following two conditions are satisfied with respect to Z(x), e(x), E and 5,. CONDITION 1: C(~)lf(~)=~(~) = qe(x)] = e(x). CONDITION 2: Ee c 5. Now, let E(x) = Es(x) = sup {p[C(x)]} be the (final) measure of error to be minimized. Then, from the above two conditions, we have f (X)G
収録刊行物
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- IEEE International Symposium on Information Theory, 2003. Proceedings.
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IEEE International Symposium on Information Theory, 2003. Proceedings. 360-360, 2003-01-01
IEEE