Design of multidimensional finite-wordlength FIR and IIR filters by simulated annealing

This paper describes a new approach to the design of multidimensional (M-D) finite-wordlength digital filters with specifications in the frequency and spatial domains. The approach is based on stochastic optimization and extends previous work on finite impulse response (FIR) filters in two ways: by inclusion of spatial constraints and by application to the case of infinite impulse response (IIR) filters. 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 filters to video processing that we are actively pursuing. Since filter coefficients are of finite precision and since the objective function is multivariable, nondifferentiable and likely to have multiple minima, we use simulated annealing for optimization. We show numerous examples of the design of practical filters such as channel and luminance/chrominance separation filters used in the NTSC system. We demonstrate the impact of coefficient precision as well as of group delay and step response constraints on filter parameters