Design of 2-D multiplierless IIR filters using the genetic algorithm

When digital filters are designed with power-of-two coefficients, the multiplications can be implemented by simple shifting operations. For VLSI implementations, multiplierless filters are faster and more compact than filters with multipliers. In this paper, the genetic algorithm (GA) is used to design two-dimensional (2-D) IIR multiplierless filters. The 2-D filter is designed to have periodically shift variant (PSV) coefficients. This increases the degrees of freedom for the multiplierless coefficients so that a better approximation can be achieved. The design involves finding the impulse response of the 2-D PSV filter in closed form and then using the GA to find the filter coefficients. Two different types of GA are used, namely, the Binary-GA and the Integer-GA. Some design examples are presented to illustrate the results.