I want to sample a signal whose derivative I know to be bounded by physical constraints. The sampling is disturbed by gaussian noise, hence I need to filter the sample with a lowpass filter. Since I know precisely the bound on the derivative magnitude, I was wondering if there is a way to translate this bound in a frequency bound, in order to determine the cutoff-frequency of the filter. My intuitive idea is that the low frequencies make up the "smooth" part of the sample (i.e. the part with a derivative that is compatible with the bound, the signal), while the higher frequencies are responsible for the sudden changes in the sample (i.e. the part with a slope that exceeds the bound, the noise); so, I think there should be a relation between the derivative and the frequency components of the sample. I'm looking for something that formalizes this concept. Thanks!

I want to sample a signal whose derivative I know to be bounded by physical constraints. The sampling is disturbed by gaussian noise, hence I need to filter the sample with a lowpass filter.

Since I know precisely the bound on the derivative magnitude, I was wondering if there is a way to translate this bound in a frequency bound, in order to determine the cutoff-frequency of the filter.

My intuitive idea is that the low frequencies make up the "smooth" part of the sample (i.e. the part with a derivative that is compatible with the bound, the signal), while the higher frequencies are responsible for the sudden changes in the sample (i.e. the part with a slope that exceeds the bound, the noise); so, I think there should be a relation between the derivative and the frequency components of the sample. I'm looking for something that formalizes this concept. Thanks!