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

Analytical methods are developed for choosing the coefficients of the first-order McClellan transformation for the design of two-dimensional (2-D) circularly symmetric digital filters from one-dimensional digital filters. New, extremely simple formulas for finding the original and the scaling free coefficients are presented. They are derived by forcing the lower-order significant terms in the power series expansion of the linear error function to zero. Formulas are also derived for finding N-D McClellan´s coefficients for the design of N-D approximately spherically symmetric digital filters. Many examples are provided to demonstrate the application of the formulas. The coefficients obtained approximate a circular contour with a higher degree of accuracy than the McClellan coefficients. The number of multiplications required to implement the designed filters is shown to be small. The formulas are very useful for real-time adaptive filter design and filtering by low-cost, stand-alone 2-D signal processors