By Yasumichi Hasegawa
This monograph offers with approximation and noise cancellation of dynamical platforms which come with linear and nonlinear input/output relationships. It additionally take care of approximation and noise cancellation of 2 dimensional arrays. will probably be of designated curiosity to researchers, engineers and graduate scholars who've really good in filtering concept and method thought and electronic pictures. This monograph consists of 2 elements. half I and half II will take care of approximation and noise cancellation of dynamical structures or electronic photos respectively. From noiseless or noisy facts, relief could be made. a style which reduces version info or noise used to be proposed within the reference vol. 376 in LNCIS [Hasegawa, 2008]. utilizing this system will enable version description to be taken care of as noise aid or version relief with no need to trouble, for instance, with fixing many partial differential equations. This monograph will suggest a brand new and straightforward approach which produces an identical effects because the strategy taken care of within the reference. As evidence of its valuable influence, this monograph presents a brand new legislation within the experience of numerical experiments. the hot and simple technique is accomplished utilizing the algebraic calculations with out fixing partial differential equations. For our goal, many genuine examples of version info and noise relief may also be provided.
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Extra info for Algebraically Approximate and Noisy Realization of Discrete-Time Systems and Digital Images
The law is said to be a law of a constrained least square. (3) : The algebraic CLS method determines the coeﬃcients of linearly dependent vectors such that the error between the approximate signal and the original signal has a minimum value in the sense of a square norm while conserving the crossed angle. Intuitively, our several examples for the algebraically noisy realization problem show that the smaller the ratio of the matrices is, the smaller the error to signal ratio is. 01 ratio of the matrix norm.
Allowing for this, we could discuss algebraically approximate and noisy realization problems for linear systems with a uniﬁed method. Since our determination method of the dimensions for linear systems is directly executed without any restrictions, our method is very useful and convenient for both approximate realization, equivalency, model reduction, and noisy realization problems. 19. 30. In multivariable analysis which is a traditional method for analysis in economics, biology, psychology and others, it is known that the factor number is determined by the number of eigenvalues of the covariance matrix which are greater than one.
2 This system completely reconstructs the original system. We can show that the algorithm for approximate realization given by the analytic CLS method in the reference [Hasegawa, 2008] produces the same systems as the above ones in the sense of the numerical calculation. For reference, in the following, we list the mean values of the sum of the square for the original signal, the obtained signal and the error to signal ratio. This table indicates that the 3-dimensional linear system reconstructs the original signal with a 4 % error to signal ratio, and the 4-dimensional linear system completely reconstructs the original system.