How to perform derivative of a random signal without finite difference schemes?

I have a random signal measured through experiments. When I perform derivative of signal using diff or gredient, these functions induce a lot of error damaging the derivative. So, is there any alternative way to perform derivative of a signal in matlab?

Answer 1

[Star Strider]

The derivative operation is by definition a highpass filter, and so will accentuate the noise. One option might be to filter the data with a lowpass filter first (there are several options), then calculate the derivative numerically.

Answer 2

[Jan]

You can try a Savitzky-Golay-Derivative filtering: https://www.mathworks.com/matlabcentral/fileexchange/30299-savitzky-golay-smooth-differentiation-filters-and-filter-application

Answer 3

[Walter Roberson]

https://math.mit.edu/~stevenj/fft-deriv.pdf

You can create blocks of signal, perhaps perform some windowing function on the blocks, and use fft techniques to estimate the derivatives over the time interval. The shorter the signal blocks, the less precise the coefficients will be, but also more reactive to changes in the signal.