METEOR: a constraint-based FIR filter design program

It is proposed to specify a filter only in terms of upper and lower limits on the response, find the shortest filter length which allows these constraints to be met, and then find a filter of that order which is farthest from the upper and lower constraint boundaries in a minimax sense. The simplex algorithm for linear programming is used to find a best linear-phase FIR filter of minimum length, as well as to find the minimum feasible length itself. The simplex algorithm, while much slower than exchange algorithms, also allows the incorporation of more general kinds of constraints, such as concavity constraints (which can be used to achieve very flat magnitude characteristics). Examples are given to illustrate how the proposed and common approaches differ, and how the proposed approach can be used to design filters with flat passbands, filters which meet point constraints, minimum phase filters, and bandpass filters with controlled transition band behavior.>