Optimisation of the response time of averaging filters

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Abstract
For the measurement of steady or slowly varying signals in the presence of unwanted noise, an ideal smoothing filter can be derived. This filter exhibits the shortest settling time for a given reduction of the noise. Rational transfer function approximations have been described which give good performance. These were derived by classical functional approximation techniques. This paper demonstrates that further improvements are possible by direct numerical optimisation of the final settling to within a specified tolerance. If this tolerance is 0.1%, a third-order optimised filter provides almost three times the measuring rate of a simple first-order low-pass network.

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