General McClellan Transformation for Designing 2-D Complex FIR Digital Filters by Genetic Algorithm Approach

A powerful genetic algorithm (GA) approach is proposed to determine the optimal coefficients of McClellan transformation. It can be used to design any arbitrary shape transformation contours to map from one-dimensional (1-D) prototypes to two-dimensional (2-D) finite-duration impulse response (FIR) filters very effectively. Certain conditions are composed such that the scaling of the transformation can be avoided. Furthermore, a generalized McClellan transformation is presented, so it can be applied to design 2D FIR filters with complex coefficients. One numerical design example is given to demonstrate the usefulness and effectiveness of the present method.