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 2D multiplierless filters. The 2D 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 2D 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.