Circulant Matrix Factorization Based on Schur Algorithm for Designing Optical Multimirror Filters

概要

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We propose a Schur-type algorithm that includes spectral factorization of covariance matrix using circulant matrix factorization to design optical multimirror filters. The Schur algorithm is the method used for a fast Cholesky factorization of the Toeplitz matrix, which can determine the reflection coefficient of optical multimirror structures. Circulant matrix factorization is a very powerful tool used for spectral factorization from the covariance polynomial using matrix manipulation in vector space that can be found in the minimum phase polynomials without using the polynomial root finding method. We present a detailed description of the circulant matrix factorization for the reciprocal polynomial approximation of an arbitrary curve (or spectrum). The Schur algorithm can, in turn, be applied to obtain the desired reflection coefficient of the optical filters. We also verify the performance of the proposed method by comparing it with the polynomial root finding method.
Published by the Japan Society of Applied Physics through the Institute of Pure and Applied Physicsの論文
2006-06-15