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This paper presents a novel technique for particle swarm optimization (PSO) of FRM FIR digital filters over the CSD multiplier coefficient space. In this technique, a FRM FIR digital filter is represented as a point in a multidimensional CSD multiplier coefficient space. In order to limit the search space, a CSD LUT is generated to include promising points in the multidimensional multiplier coefficient space. Candidate CSD FRM FIR digital filters generated in the course of particle swarm optimization are guaranteed to remain automatically within the CSD LUT boundaries during the constituent PSO move operation without any recourse to backtracking. This is achieved by augmenting the LUT with barren regions. An example is given to illustrate the application of the proposed PSO to the design of a lowpass FRM FIR digital filter.