Design of optimal digital FIR filters with arbitrary magnitude and phase responses

This paper presents a new multiple-exchange ascent algorithm for designing optimal Chebyshev digital FIR filters with arbitrary magnitude and phase specifications. Compared to existing Chebyshev design techniques, the new design algorithm exhibits faster convergence while maintaining high accuracy, and is guaranteed to converge to the optimal solution. In addition, the proposed algorithm reduces to the classic second Remez (Parks-McClellan) algorithm when real-only or imaginary-only filters are designed and is, therefore, a true generalization of the classic Remez algorithm to the complex case.