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Root-exchange property of constrained linear predictive models

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1 Author(s)
Backstrom, Tom ; Lab. of Acoust. & Audio Signal Process., Helsinki Univ. of Technol., Espoo, Finland

In recent works, we have studied linear predictive models constrained by time-domain filters. In the present study, studied the one-dimensional case in more detail. Firstly, we obtain root-exchange properties between the roots of an all-pole model and corresponding constraints. Secondly, using the root-exchange property we can construct a novel matrix decomposition ATRA# = I, where R is a real positive definite symmetric Toeplitz matrix, superscript # signifies reversal of rows and I is the identity matrix. In addition, there exists also an inverse matrix decomposition CTR-1C# = I, where C ∈ C is a Vandermonde matrix. Potential applications are discussed.

Published in:

Statistical Signal Processing, 2003 IEEE Workshop on

Date of Conference:

28 Sept.-1 Oct. 2003