Mathematica 9 is now available

Filter Design

download notebookDownload this example as a Mathematica notebook.

Digital Image Processing allows you to design both one- and two-dimensional custom FIR filters and to solve even the hardest image filtering problems.


A common method of obtaining 2D filters is to obtain them indirectly by transforming 1D prototypes. The simplest method imposes rectangular symmetry on the resulting 2D filter by taking the outer product of two 1D filters. In order to obtain a circularly symmetric 2D filter from a 1D prototype, the common approach is to use the McClellan transformation, also known as the frequency transformation [1]. The resulting filters have good performance as well as circular symmetry. They have also been shown to be optimal under a restricted set of conditions. Here we use the McClellan transformation to transform a 1D equiripple filter to a circularly symmetric 2D filter. The prototype filter is lowpass.


This calculates the magnitude spectrum of the 2D lowpass filter using a 128-point DFT.


This plots one quadrant of the magnitude spectrum.




[1] McClellan, J. "The Design of Two-Dimensional Digital Filters by Transformations," Proceedings of the Annual Princeton Conference on Information Sciences and Systems 7 (1973) 247-251.