Roundoff Noise Minimization for a Class of 2-D State-Space Digital Filters Using Joint Optimization of High-Order Error Feedback and Realization

Akimitsu DOI  Takao HINAMOTO  Wu-Sheng LU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.9   pp.1918-1925
Publication Date: 2014/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.1918
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
Fornasini-Marchesini's second model,  high-order error feedback and realization,  joint optimization,  roundoff noise minimization,  2-D filters,  

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Summary: 
For two-dimensional IIR digital filters described by the Fornasini-Marchesini second model, the problem of jointly optimizing high-order error feedback and realization to minimize the effects of roundoff noise at the filter output subject to l2-scaling constraints is investigated. The problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem is then solved iteratively by applying an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. Finally, a numerical example is presented to illustrate the validity and effectiveness of the proposed technique.