McClellan transform based design techniques for two-dimensional linear-phase FIR filters

This paper considers the design problem of two-dimensional (2-D) linear-phase FIR digital filters through the use of the McClellan transform method. We present two methods for determining the coefficients of the McClellan transform when designing 2-D linear-phase FIR digital filters with continuous and powers-of-two coefficients, respectively. Based on the proposed methods, the contour approximation for 1-D (one-dimensional) to 2-D digital filter transformation and finding the band-edge frequencies of the corresponding 1-D FIR digital filter can be achieved simultaneously. This results in that the required complexity of the designed 2-D digital filter satisfying the design specifications can be minimized. Moreover, the proposed methods allow us to employ the McClellan transform with order more than one for enhancing the capability of the original McClellan transform. Considering the determination of the McClellan transform coefficients and the band-edge frequencies for the design, we formulate the design problem as a linear programming optimization problem. Then, an efficient design procedure is presented to avoid the use of time consuming simplex algorithms. For the powers-of-two coefficient design, a discrete design procedure is presented to avoid the use of time-consuming mixed integer linear programming algorithms. Computer simulations for showing the effectiveness of the proposed design techniques are also presented.