Abstract

The usual way of designing a lter is to specify a lter length and a nominal response, and then to nd a lter of that length which best approximates that response. In this paper we propose a di erent approach: specify the lter only in terms of upper and lower limits on the response, nd the shortest lter length which allows these constraints to be met, and then nd a lter of that order which is farthest from the upper and lower constraint boundaries in a mini-max sense. Previous papers have described methods for using an exchange algorithm for nding a feasible linear-phase FIR lter of a given length if one exists, given upper and lower bounds on its magnitude response. The resulting lters touch the constraint boundaries at many points, however, and are not good nal designs because they do not make best use of the degrees of freedom in the coe cients. We use the simplex algorithm for linear programming to nd a best linear-phase FIR lter of minimum length, as well as to nd the minimum feasible length itself. The simplex algorithm, while much slower than exchange algorithms, also allows us to incorporate more general kinds of constraints, such as concavity constraints (which can be used to achieve very at magnitude characteristics). We give examples that illustrate how the proposed and the usual approaches di er, and how the new approach can be used to design lters with at passbands, lters which meet point constraints, minimum phase lters, and bandpass lters with controlled transition band behavior. 1.

Citations