Optimal Integer Order Approximation of Fractional Order Filters

Fractional order filters have been studied since a long time, along with their applications to many areas of physics and engineering. In particular, several solutions have been proposed in order to approximate their frequency response with that of an ordinary filter. In this paper, we tackle this problem with a new approach: we solve analytically a simplified version of the problem and we find the optimal placement of poles and zeros, giving a mathematical proof and an error estimate. This solution shows improved performance compared to the current state of the art and is suitable for real-time parametric control.