Design of multidimensional nite-wordlength FIR and IIR lters by simulated annealing

This paper describes a new approach to the design of multidimensional (M-D) nite-wordlength digital lters with speciications in the frequency and spatial domains. The approach is based on stochastic optimization and extends previous work on nite impulse response (FIR) lters in two ways: by inclusion of spatial constraints and by application to the case of innnite impulse response (IIR) lters. The formulation proposed is based on a multiple-term objective function that, in addition to magnitude constraints, also includes step response, group delay and stability constraints. Our attention to these characteristics stems from the application of such lters to video processing that we are actively pursuing. Since lter coeecients are of nite precision and since the objective function is multivariable, non-diierentiable and likely to have multiple minima, we use simulated annealing for optimization. We show numerous examples of the design of practical lters such as channel and luminance/chrominance separation lters used in the NTSC system. We demonstrate the impact of coeecient precision as well as of group delay and step response constraints on lter parameters.