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Trying to display bandwith via Math on Siglent SDS2k+/2kHD/800X HD
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Performa01:
The “stuff in the handbook” is most likely a (copy&paste) leftover from prehistoric manuals dating back to long forgotten times, when math and measurements were performed on screen data.

The “Dx” parameter in the SDS2000X Plus math refers to sample points and we actually need to take the sample rate into account whenever we want to convert it to an absolute time.
However, this is a deep memory scope; a sensible setting for the max. record length is 10/20 MPts, which results in a constant sample rate up to 1 ms/div, i.e. a record length of 10 ms. Heck, if the need should be, this could even be extended to 100 ms by selecting 100/200 MPts in the Acquire menu. I very much doubt that many users will have the need for the derivative function on slow waveforms <10 Hz and then at frequently changing horizontal time bases.

The little but more advanced brother SDS2000X HD already offers a constant sample rate setting just like the SDS6000. This can solve any problems and situations, where a function depends on the sample rate.

Regarding the attempts to get the frequency response from a fast risetime pulse, there are a number of reasons, why it doesn’t work as expected on the SDS2000X Plus right now.

1.   The scale is wrong. The FFT-sample rate is increased by two orders of magnitude whenever the argument is a derivative. This bug seems to be exclusive to the SDS2000X Plus.
2.   The input field of the formula editor is limited, so we just cannot add the average function there. But this is mandatory to get a nice and clean frequency response graph. On the other Siglent scopes we can use the average acquisition mode, so the lengthy expression “average()” does not eat up precious formula space.

A longer formula string has already been requested. I’ve also reported the FFT bug today.
Performa01:
Here’s a demonstration what the SDS2504X HD looks like with a moderate ~500ps risetime pulse coming from the SDG7102A. 32x averaging before up-sampling.

gf:

--- Quote from: Performa01 on May 17, 2022, 08:52:53 am ---The “Dx” parameter in the SDS2000X Plus math refers to sample points and we actually need to take the sample rate into account whenever we want to convert it to an absolute time.

--- End quote ---

At 20ns/div and 10ns/div, FFT(Cx) shows a sample rate of 50GSa/s, and at 5ns/div it shows a sample rate of 200GSa/s.
This is obviously the interpolated sample rate, and it seems that interpolation joins in automatically at <= 20ns/div.

What is dx=4 now supposed to mean at (say) 10ns/div? Still 2ns (4 / 2 GSa/s), or 80ps (4 / 50 GSa/s)?

EDIT: Looking at the image in your previous message it must be (significantly) less than 2ns, otherwise the spectrum would look different. But is it 80ps then?
rf-loop:

--- Quote from: Performa01 on May 17, 2022, 09:08:51 am ---Here’s a demonstration what the SDS2504X HD looks like with a moderate ~500ps risetime pulse coming from the SDG7102A. 32x averaging before up-sampling.

--- End quote ---
Perhaps marker 1 horizontal position is better in ≥ 1/2 Δf 
(also looks weird your marker 2 vertical position looks like below trace level)
gf:
Related to the frequency response calculation I also wonder:

* Is it possible to add/subtract/multiply/divide freqency domain traces (results of FFT) with math functions?
* If yes, in which space is the operation carried out? Complex, linear magnitude, log magnitude (dB)?
* Is it possible to load an (externally and synthetically generated) trace from e.g. USB stick, and use it as argument to math functions?
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