Design of 2-D multiplierless filters using the genetic algorithm

When digital filters are designed with power-of-two coefficients, the multiplications can be implemented by simple shifting operations. In this paper, the genetic algorithm (GA) is used to design 2-D 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 concepts.