Equiripple Approximation Of Fan Filters
James H. McClellan, Thomas W. Parks · Geophysics · 1972
Abstract An efficient procedure for the approximation of two-dimensional (2-D) fan filters is presented. The Chebychev (or min-max) error criterion is used to measure the optimality of the approximation as opposed to previous designs which use the least-squares norm. Since the direct solution of a 2-D Chebychev approximation problem is difficult, a change of variables is introduced to convert the 2-D approximation problem into an equivalent 1-D low-pass filter approximation problem. The response is opptimized in the 1-D domain, and then the change of variables is applied to obtain the 2-D filter. Thus the techniques of 1-D Chebychev approximation are applied to yield a 2-D fan filter.