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I am trying to recover a laser beam profile using numerical differentiation of the data obtained from a "knife-edge scan". I am trying to select between two different methods to smooth out the numerical noise.

Here is my raw data and the derivative:

Here, I arbitrarily chose the 13 points, 4th order Savitzky-Golay method.

And here is the frequency spectrum of the derivative:

I have read that high frequencies caused purely by noise can be identified and removed in Fourier space, while the noise contamination of the low order components cannot be eliminated. So, in my spectrum how do we tell where the noise band starts?

Due to instrumental limitations, I am restricted to 2 decimal places when making measurements. If we had data with more significant figures, would that make the noise band more discernable?

In general, how does the Fourier smoothing compare to the Savitzky-Golay method?

Here is my raw data and the derivative:

Here, I arbitrarily chose the 13 points, 4th order Savitzky-Golay method.

And here is the frequency spectrum of the derivative:

I have read that high frequencies caused purely by noise can be identified and removed in Fourier space, while the noise contamination of the low order components cannot be eliminated. So, in my spectrum how do we tell where the noise band starts?

Due to instrumental limitations, I am restricted to 2 decimal places when making measurements. If we had data with more significant figures, would that make the noise band more discernable?

In general, how does the Fourier smoothing compare to the Savitzky-Golay method?