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I have a sensor producing bandlimited data at a predictable periodic rate, corrupted by IID white noise (at least over relatively short periods of time). There is also a slowly time-varying bias, which can safely be ignored as it is several orders of magnitude smaller than the white noise.

I want to numerically differentiate the sensor data. The estimate must be causal. Wikipedia has a nice page on the topic along with filter coefficients for deterministic functions.

Is this set of coefficients good in the presence of noise, or is there a better way to perform this estimate? What factors will the new method depend on?

Edit:

Ideally, the method will be computationally cheap as it will be run at a high rate on an embedded platform ...

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I have used the algorithm described in this paper with great success.

This method uses Tikhonov regularization of the total variation of the signal. It is parameterized, so you can easily adjust the sensitivity as needed.

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    Emily, did you have any success with your 1D version of the filter?2018-05-15