In this paper, we prove the Plancherel-Rotach asymptotic formula for the chebyshev-hermite functions (-1)(n)e(x2/2) (e(-x2)) ((n)) root2(n)n!rootpi and their derivatives for the case in which +infinity belongs to the ...
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In this paper, we prove the Plancherel-Rotach asymptotic formula for the chebyshev-hermite functions (-1)(n)e(x2/2) (e(-x2)) ((n)) root2(n)n!rootpi and their derivatives for the case in which +infinity belongs to the domain of definition. A method for calculating the approximation accuracy is also given.
The paper deals with a development of an analytical device's signal processing algorithms based on decomposition signals into the coefficients of the basis of orthogonal functions. The chebyshev-hermite functions ...
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ISBN:
(纸本)9781728167008
The paper deals with a development of an analytical device's signal processing algorithms based on decomposition signals into the coefficients of the basis of orthogonal functions. The chebyshev-hermite functions are used as decomposition basis. Two different algorithms (traditional and hierarchical) for decomposition analytical device's signal are described. The traditional one is used to obtain coefficients of decomposition of the analytical device's signal in chosen basis with selected number of basis functions. The hierarchical one is used to obtain decomposition coefficient first with only zero-order basis function, then compute the difference between signal and its copy reconstructed by just obtained decomposition coefficient. Further, the described procedure is repeated for computed earlier difference with first-order basis function and so on, until the difference is below the selected value. The main goal of the current paper is to compare the hierarchical approach with the traditional one in terms of accuracy and computation time.
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