Chebyshev design of linear-phase FIR filters with linear equality constraints

By using basis transformation, the Chebyshev approximation of linear-phase finite-impulse response (FIR) filters with linear equality constraints can be converted into an unconstrained one defined on a new function space. However, since the Haar condition is not necessarily satisfied in. the new function space, the alternating property does not hold for the solution to the resulted unconstrained Chebyshev approximation problem. A sufficient condition for the best approximation is obtained in this brief, and based on this condition, an efficient single exchange algorithm is derived for the Chebyshev design of linear-phase FIR filters with linear equality constraints. Simulations show that the proposed algorithm can converge to the optimal solution in most cases and to a near-optimal solution otherwise. Design examples are presented to illustrate the performance of the proposed algorithm.