On anti-aliasing filtering and over-sampling scheme in system identification

- Traditional anti-aliasing filtering procedure is shown to give inconsistent estimate.
- New identification method is proposed based on the over-sampling scheme.
- Anti-aliasing is achieved in both open-loop and closed-loop identification.
- Extra excitation is achieved from high frequency noise in closed-loop identification.
- Exact condition is given for accuracy increase with higher sampling frequency.

In this work, two fundamental issues in system identification, sampling frequency and anti-aliasing filtering are revisited, questions like, “Can higher sampling frequency help increase model accuracy?”, and, “Can we do better than anti-aliasing filtering?” will be answered. First it is shown that, the traditional anti-aliasing filtering procedure does not give a consistent estimate of the desired model. Then an identification method is proposed based on the over-sampling scheme where a high frequency model is first identified and then converted to the (lower) control sampling frequency. It is shown that when the output noise contains energy beyond the bandwidth of the plant, the proposed method performs anti-aliasing in both open-loop and closed-loop identification; and in closed-loop identification, extra excitation is achieved from the high frequency noise. Simulation studies are used to illustrate the findings. The result has important implications in control applications.