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

摘要

Simple analytical and exact relations for a direct determinationnof the natural modes of the Cauer filters of the order n=2l3nm; l, m=0,1,2,... are derived without using Jacobian ellipticnfunctions and integral. The number of necessary floating pointnoperations used for the computation of the natural modes by the proposednalgebraic method FA, as compared with one of the mostnaccurate and efficient algorithms suggested by Parks and Burrus (1987) FnM, applied in the popular MATLAB program, shows anconsiderable advantage of the new method, with a figure of merit FMn/FA ranging from 196 to 20 for filter orders n=2 tonn=18