Filtering and differentiating noisy signals using neural networks

Measured signals are difficult to differentiate. Measurement noise, quantization and jitter occur and in general cannot be eliminated by simple lowpass filtering. This paper presents a new approach for off-line filtering and differentiating sampled time series using a special kind of neural networks, namely an extension of the local linear model tree (LOLIMOT). LOLIMOT is a tree construction algorithm based on the idea of approximating nonlinear functions by piecewise linear models. The filtered signal can be guaranteed not to leave a given band of tolerance, shows human-like smoothing effects and allows the introduction of a priori knowledge