Optimal Synthesis of a Class of 2-D Digital Filters with Minimum L2-Sensitivity and No Overflow Oscillations

Takao HINAMOTO  Ken-ichi IWATA  Osemekhian I. OMOIFO  Shuichi OHNO  Wu-Sheng LU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.7   pp.1987-1994
Publication Date: 2006/07/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.7.1987
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
L2-sensitivity minimization,  L2-scaling constraints,  no overflow oscillations,  optimal synthesis,  a class of 2-D state-space digital filters,  

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The minimization problem of an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints is formulated for a class of two-dimensional (2-D) state-space digital filters. First, the problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algorithm with closed-form formula for gradient evaluation. The coordinate transformation matrix obtained is then used to synthesize the optimal 2-D state-space filter structure that minimizes the L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints. Finally, a numerical example is presented to illustrate the utility of the proposed technique.