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Spectral Factorization

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David83

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Hi,

I have this equation:

\[g_1^*(q)h_1^*(q)g_1(q^{-1})h_1(q^{-1})+g_2^*(q)h_2^*(q)g_2(q^{-1})h_2(q^{-1})\]

where

\[g_1(q^{-1})=g_{10}+g_{11}q^{-1}+\cdots+g_{1N}q^{-N}\]

and the same for h. \[q^{-1}\] is the time delay unit, and \[q\] is the time advance unit. I need to find the spectral factorization of this in the form of \[f(q^{-1})f^*(q)\], and I have no clue how to do that. Any hint will be highly appreciated.

Regards
 

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