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- W2124618941 abstract "In this paper, with respect to band-limited signals f(t) contained in a given set of signals Ξ, we present very general optimum continuous running approximations that minimize various continuous worst-case measures of running approximation error simultaneously. Firstly, as a means of proof, we consider a multi-legged-type signal m(t) that is a combined-signal of a given infinite number of one-dimensional band-limited signals h <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> (t) (n=...,-2,-1,0,1,2,...) in Ξ. A series of given finite segments σ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> (t) of h <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> (t) are arranged sequentially and make backbone of m(t). Sets of two other signals of h <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> (t) make feet of m(t). With respect to these h <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> (t), we consider a series of the Kida's optimum approximations, g <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> (t), each of which uses a given finite number of generalized sample values of h <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> (t). Also, we define a similar multi-legged-type approximation y(t) of m(t) using these g <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> (t). Secondly, under a slight modification of Ξ, when the backbone of m(t) itself is a band-limited signal f(t) in Ξ, we prove that backbone of y(t) becomes the corresponding optimum continuous running approximation of f(t). Although this paper treats pure theoretical topics, we believe that it is important for multi-paths communication and signal processing systems, such as MIMO systems, to present a fundamental method of constructing the optimum running approximation including various extended multi-paths transmission systems without using difficult high-level mathematical concept." @default.
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- W2124618941 date "2012-05-01" @default.
- W2124618941 modified "2023-10-04" @default.
- W2124618941 title "A Simple Proof of the Generalized Optimum Continuous Running-Approximation Based on a Class of Multi-Legged-Type Signals" @default.
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- W2124618941 doi "https://doi.org/10.1109/vetecs.2012.6240274" @default.
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