This paper presents a new discrete-time sliding mode filter for effectively removing noise in control of mechatronic systems. The presented filter is an enhanced version of a sliding mode filter by employing an adaptive gain in determining a virtual desired velocity of the output. Owing to the use of backward Euler discretization, the discrete-time implementation of the filter does not produce chattering, which has been considered as a common problem of sliding mode techniques. Besides that, the state of the filter converges to the desired state in finite time. Numerical example and experimental position control of a mechatronic system are conducted for validating the effectiveness of the filter.