Some aspects of novel matrix spectral factorization algorithm

Author: Lasha Ephremidze
Co-authors: Nika Salia
Keywords: Spectral factorization
Annotation:

Recently, a new matrix spectral factorization method has been developed in [1]. A construction of special type of unitary matrix polynomials plays a key role in the developed method. The construction is actually reduced to certain system of algebraic linear equations. In the present paper, we give a simple explanation to the origin of these equations. Furthermore, in the last step of construction of the unitary matrix polynomial, one needs to invert a certain Gram matrix and it is proved in [1] that this matrix is nonsingular. In the process of software implementation of above factorization algorithm, it is preferable to be guaranteed that the Gram determinant is remote from machine precision zero. We present such estimation in the paper. [1] G. Janashia, E. Lagvilava, and L. Ephremidze, A new method of matrix spectral factorization, IEEE Trans. Inform. Theory, vol. 57, no. 4, (2011), 2318-2326, DOI: 10.1109/TIT.2011.2112233