Analytical methods for the design of 2-D elliptically symmetric digital filters using McClellan transformation

Abstract

Some analytical methods are developed for choosing the coefficients of the first-order McClellan transformation for the design of two-dimensional elliptically symmetric digital filters from one-dimensional digital filters. Several extremely simple formulas are presented for both the original and the scaling-free coefficients for all the cases of both the vertical and the horizontal elliptical cutoff contours. The formulas are derived by forcing the lower-order significant terms in the power series expansion of the linear error function to zero. Many examples are given. The results of these methods agree very well with the results of the optimization methods, and the accuracy of the formulas is more than sufficient for many engineering applications. The formulas are very useful for real-time adaptive filter design and filtering by low-cost, stand-alone two-dimensional signal processors. The number of multiplications required to implement the designed filters is shown to be small.<>