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.

Citation Download Citation

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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