A novel approach for complex Chebyshev-approximation with FIR filters using the Remez exchange algorithm

The long standing problem of the approximation of a complex-valued desired frequency response using FIR filters is investigated again. The resulting complex error is minimized in the Chebyshev sense. The proposed algorithm deals directly with the complex error function, which is a linear one. This will be done by formulating a complex interpolation task. Additionally the introduction of a complex weighting function allows a different weighting of the magnitude and the phase error. The applied method can be characterized as a generalization of the Remez exchange algorithm for a complex weighted Chebyshev-approximation. The algorithm allows the design of filters with complex as well as real coefficients at high convergence speed. The well known Chebyshev design of exactly linear phase FIR filters with real coefficients is included as a special case.