Method for FIR filters design with compressed cosine using Chebyshev's norm

摘要

This paper considers a new method for FIR filters design. The method uses an L, optimality norm. To achieve a better approximating effect, a new modulating function which compresses the oscillations of the cosine is proposed. A parameter sets the gradient of the modulating function, with respect to the oscillations' compression. The approximating polynomial is carried out using Remez' exchange algorithm. An optimal polynomial with lowest possible (four) degree, that approximates an ideal filter's response with high precision is proposed. With the proposed method a FIR filter with arbitrary specifications can be designed. Design examples of FIR filters with a minimization of calculation are performed. The obtained filter's responses are close to the ideal response. The design examples demonstrate that the proposed approach may be a good alternative in several applications.