The optimum estimation of statistical signals based on systematic expression of many types of sample arrays in multidimensional space

Yuichi Kida; Takuro Kida

doi:10.1117/12.681945

25 August 2006 The optimum estimation of statistical signals based on systematic expression of many types of sample arrays in multidimensional space

Yuichi Kida, Takuro Kida

Author Affiliations +

Proceedings Volume 6315, Mathematics of Data/Image Pattern Recognition, Compression, and Encryption with Applications IX; 63150C (2006) https://doi.org/10.1117/12.681945
Event: SPIE Optics + Photonics, 2006, San Diego, California, United States

Abstract

Extended interpolatory approximation is discussed for some classes of n-dimensional statistical signals. Firstly, we present two sufficient conditions of the optimum approximation. Then, as example of this optimum approximation, we consider approximation of n-dimensional statistical signals expressed by linear combination of the finite set of base signals in a n-dimensional space. We assume that these signals have generalized mutual moment smaller than a given positive number. Related topic was discussed in the previous paper. However, discrete running approximation along the time axis that uses shift-invariant interpolation functions with the finite supports is not treated in the previous paper. In the final part of this paper, we discuss best running approximation of n-dimensional signals expressed by linear combination of the finite set of sinusoidal signals in a n-dimensional space. The presented methods have the minimum measure of approximation error among all the linear and the nonlinear approximations using the same measure of error and generalized sample values.

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Yuichi Kida and Takuro Kida "The optimum estimation of statistical signals based on systematic expression of many types of sample arrays in multidimensional space", Proc. SPIE 6315, Mathematics of Data/Image Pattern Recognition, Compression, and Encryption with Applications IX, 63150C (25 August 2006); https://doi.org/10.1117/12.681945

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