A New Filter Based on Sliding Mode Method with Discrete-Time Implementation for Noise Attenuation and Differentiation

This paper presents a novel filter based on the sliding mode method for filtering noise and extracting reliable signals from noisy signals by enhancing Levant's sliding mode filter. Specifically, the proposed sliding mode filter takes advantage of the generalized signum function to adjust the gain in different regions of phase space, thereby decreasing the overshoot during the response phase. Additionally, the discrete-time implementation of the proposed sliding mode filter is achieved by utilizing the implicit-Euler algorithm, which effectively eliminates chattering in the output. The effectiveness of the presented sliding mode filter is substantiated via numerical simulation cases.