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

Hinamoto Takao

Ohnishi Hiroaki

Lu Wu-Sheng

IEEE Transactions on Signal Processing

The joint optimization problem of error feedback and realization for two-dimensional (2-D) state-space digital filters to minimize the effects of roundoff noise at the filter output subject to L2-norm dynamic-range scaling constraints is investigated. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem at hand is then solved iteratively by applying an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. Analytical details are given as to how the proposed technique can be applied to the cases where the error-feedback matrix is a general, block-diagonal, diagonal, or block-scalar matrix. A case study is presented to illustrate the utility of the proposed technique.

Error feedback

joint optimization

L2-scaling constraints

roundoff noise minimization

state-space realization

2-D digital filters

Electrical engineering [ 540 ]

eng

IEEE

Copyright (c) 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted componet of this word in other works must be obtained from the IEEE.

[ISSN] 1053-587X

[DOI] 10.1109/TSP.2006.881178

[NCID] AA10788333

[DOI] http://dx.doi.org/10.1109/TSP.2006.881178