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Mathematical methods in signal processing for spectral estimation

Abstract : We study the theory and the application for a multiple of methods in the domain of spectral power estimation. In the 1 D case, the Levinson and Burg approach are exposed into the saine theoretical and numerical context. In the 2D case, and the general ND case new methods are proposed for spectral power estimation following the criteria of an associated positive definite ND correlation matrix extension, and the Maximum of Entropy spectral power measure. Also, ND Toeplitz correlation systems are exposed in the context of the generalized reflection coefficients for the block Toeplitz case and the Toeplitz block Toeplitz case. In both cases, corresponding algorithms are proposed for the solution of the autoregressive ND linear system. The ND Toeplitz correlation matrix structure is studied under two conditions. The first is the infinite positive extension support with an approximate matching property. The second is a positive extension with a Maximum of Entropy property. Following the second condition, we formalize a fundamental positiveness theory establishing the correspondence between a minimum group of reflection coefficients and the ND Toeplitz correlation matrix, with the saine degree of liberty.
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Contributor : Ens Cachan Bibliothèque <>
Submitted on : Monday, March 12, 2007 - 11:36:05 AM
Last modification on : Monday, February 15, 2021 - 10:48:58 AM
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  • HAL Id : tel-00136093, version 1


Rami Kanhouche. Mathematical methods in signal processing for spectral estimation. Mathematics [math]. École normale supérieure de Cachan - ENS Cachan, 2006. English. ⟨tel-00136093⟩



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