On the Factorization of Rational Discrete-Time Spectral Densities
On the Factorization of Rational Discrete-Time Spectral Densities
In this paper, we consider an arbitrary matrix-valued, rational spectral density Φ(z). We show with a constructive proof that Φ(z) admits a factorization of the form Φ(z)=W <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> (z <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ) W(z), where W(z) is stochastically minimal. Moreover, W(z) and its right inverse are analytic in …