Design of Two-Dimensional Zero-Phase FIR Digital Filter by McClellan Transformation and Interval Global Optimization

The McClellan transformation is widely used to design the 2-D FIR filters. It is an essential task to determine the transform coefficients so that the square errors are minimized. This issue can be viewed as a nonlinear optimization problem with constraint conditions. This brief proposed the interval analysis (IA) to solve this nonlinear optimization problem. There are two distinguishing features of the proposed method when compared with conventional methods, such as quadratic programming, eigenfilter approach or Lagrange multiplier method, etc. First, the transform parameters are obtained by minimizing the integral of the squared errors along the desired contour, instead of discrete sampling. Second, the IA guarantees that the constraint conditions could be always satisfied, thus ensuring the reliability of the optimization. A 2-D fan filter and a diamond-shaped filter are designed, which demonstrate the feasibility of the presented method; images are processed to verify the effectiveness of the designed 2-D fan filter.