There are many applications for which a robotic device is used to recreate the sense of touch for a physical or virtual environment. Transparency and stability are two major issues in controlling haptic devices. Transparency highly depends on the quality of state observation while the stability range is mainly affected by the time-delay and sampling frequency. The control force is calculated based on the model of the environment and usually is a function of the position and the velocity at the joints. Optical encoders are commonly used for position measurement because of their high resolution, robustness to noise, and high bandwidth. The velocity, however, is usually determined by differentiating the position data over time which can be noisy at high frequencies. This noise demotes the transparency and stability. Low-pass filters are widely used to filter the noise but they make the system slow and conservatively introduce time-delay which further limits the stability range. In this paper, the method of Adaptive Frequency Differentiation (AFD) is introduced, which operates at varying frequencies and effectively removes the noise caused by the error in position data. The AFD is optimized to operate at its best performance while maintaining the reliability of the differentiation. The output of the AFD is derived by logically interpreting the available data and does not involve iterative loops, which improves the processing time. An extension to this method allows to compute low-delay and noiseless acceleration directly from the position data. The claims of this paper are supported by simulation and experimental results.