Low complexity two-dimensional digital filters using unconstrained SPT term allocation

Previous work by the authors has demonstrated how circularly symmetric and diamond-shaped low-pass linear phase 2-D FIR filters can be designed using coefficients comprising the sum or difference of two signed power-of-two (SPT) terms. This has employed a minimax error criterion in conjunction with an optimisation process based on the use of genetic algorithms. The resulting filters exhibit superior performance to those designed using other methods reported such as simulated annealing and linear programming. This paper extends this work by demonstrating the further improvements possible if the constraints are relaxed, such that only the overall number of SPT terms is constrained, while the distribution between filter coefficients is unconstrained.