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An algebraic solution to the spectral factorization problem

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1 Author(s)
Anderson, B.D.O. ; University of Newcastle, Newcastle, N.S.W., Australia

The problem of giving a spectral factorization of a class of matrices arising in Wiener filtering theory and network synthesis is tackled via an algebraic procedure. A quadratic matrix equation involving only constant matrices is shown to possess solutions which directly define a solution to the spectral factorization problem. A spectral factor with a stable inverse is defined by that unique solution to the quadratic equation which also satisfies a certain eigenvalue inequality. Solution of the quadratic matrix equation and incorporation of the eigenvalue inequality constraint are made possible through determination of a transformation which reduces to Jordan form a matrix formed from the coefficient matrices of the quadratic equation.

Published in:

Automatic Control, IEEE Transactions on  (Volume:12 ,  Issue: 4 )

Date of Publication:

August 1967

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