Exact determination of the natural modes of some Cauer filters by means of a standard analytical procedure

Simple analytical and exact relations for a direct determination of the natural modes of the Cauer filters of the order n=2/sup l/3/sup m/; l, m=0,1,2,... are derived without using Jacobian elliptic functions and integral. The number of necessary floating point operations used for the computation of the natural modes by the proposed algebraic method F/sub A/, as compared with one of the most accurate and efficient algorithms suggested by Parks and Burrus (1987) F/sub M/, applied in the popular MATLAB program, shows a considerable advantage of the new method, with a figure of merit F/sub M//F/sub A/ ranging from 196 to 20 for filter orders n=2 to n=18.