Abstract
Algorithm of complex signal decomposition on elementary components having Lorenz form is proposed.The non-linear minimization problem to the problem of linear equation solving. The number of components is the necessary aprioir information. The algorithm can be combined with the method of statistical regularization. The results of numerical experiments are represented.
Highlights
The complex signal decomposition on elementary component is the problem of the interest of many fields: spectroscopy, chemometric, radiophysics etc. [1,2,3,4,5,6]
Рассмотрим Algorithm of complex signal decomposition on elementary components having Lorenz form with some transformation of non-linear minimization problem to the problem of linear equation solving
(8) is the system of linear equations with 4m-1 unknown quantities: 2m unknown quantities xj and 2m-1 unknown quantities zk
Summary
And later ’ near the product symbol indicates that multiplier with i=j is eliminate of the product. (3) can be represented in the form:. And later ’ near the product symbol indicates that multiplier with i=j is eliminate of the product. (3) can be represented in the form:. Φ(ω)∏(ω −Wj )(ω −= Wj*) ∑ ai∏ '(ω −Wj )(ω −Wj*). Let us to introduce the new variables xi , zk (i=1,2,....,2m), (k=1,2,...,2m-1), defined by: m. Taking into account (5.6) and (5.7) the equation (5.1) can be represented in the form: Φ(ω)(ω2m + x1ω2m−1 + ... (8) is the system of linear equations with 4m-1 unknown quantities: 2m unknown quantities xj and 2m-1 unknown quantities zk. After that the parameters ai can be found from linear equations system. The complex polynomial (5.9) roots can be found by Berstow method [7]. For noise removal can be used the regularized multistep support vector method [8]
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