Complex Chebyshev Approximation for FIR Digital Filters

In many applications of digital signal processing, the complex Chebyshev approximation of digital filters is important that approximates simultaneously the magnitude and phase responses, and then the design method is required. This paper presents an efficient design method for the complex Chebyshev approximation of FIR digital filters. In the proposed method, the design problem is formulated in the form of the linear problem by using the Remez exchange algorithm extended to the complex domain. Moreover, for reduction of computational complexity, the frequency response is obtained by using the Lagrange\u27s interpolation formula in each step of the iteration process. It is clear that the proposed method has a comparable frequency response with a fewer computational complexity than the conventional methods