Chebyshev design of FIR filters with arbitrary magnitude and phase responses

This paper presents a method for the design of nonlinear phase FIR digital filters with complex or real-valued coefficients using the Chebyshev error criterion. Three different problems are considered: Complex Chebyshev approximation with additional weighting of the resulting magnitude and phase errors, simultaneous Chebyshev approximation of a given magnitude and phase response, and simultaneous Chebyshev approximation of a given magnitude and group delay response. A linearization approach leads to a problem formulation that allows the use of stable algorithms with guaranteed convergence. It is shown that for this linear approach the simultaneous Chebyshev approximation of a desired magnitude and phase response is a special case of complex Chebyshev approximation with independent weighting of the magnitude and phase errors. Two existing design methods are included in this method as special cases.