Here are a couple of screenshots from my Lecroy WavePro 960 (2 GHz, 16 GS/s).

Trace "A" is an average of the channel under test (for noise reduction).

Trace "B" is the derivative d/dt of A. Note the vertical scale of 1 GV/s per div!

Trace "C" is the FFT of B.

Trace C gives the frequency response of the oscilloscope and pulser (and any cable connecting them, none in this case).

Trace A shows rise time of 268 ps. Using the relation 0.45/Tr=BW, it estimates 1.68 GHz. Obviously such rules of thumb are not universally applicable. The actual -3 dB point in Trace C is 2.03 Ghz.

It can be shown mathematically that an impulse has equal energy at all frequencies. So, if you pass an impulse through a system, you can measure the frequency response by looking at what went through. Generating an actual impulse is impractical, largely because generating one with enough energy to measure practically presents difficulties. For example, an impulse that delivering the same energy to the system as does a 50 ps 1 V rising edge, would require a 50 ps wide, 20 000 000 000 volt pulse. I can't generate 20 GV in my lab, and my scope input wouldn't like it if I could

Actually, we don't quite need that much energy but it is still difficult to generate a well-behaved impulse. Fortunately, we can use math trickery instead. We know that the d/dt of a step is an impulse. The "d/dt of the response to a step" is the same as the "response to the d/dt of a step" (response to an impulse). So we apply a fast rise step to the system, measure system step response, then take d/dt of the step response to get the system impulse response. Then convert to frequency domain (take FFT) to get frequency response. That is exactly what is shown in Trace C.

In this case, the frequency response can be seen varying about +/- 1 dB from zero to 2 GHz, and dropping extremely rapidly after 2 GHz. The -3 dB point relative to DC is 2.03 GHz.

I have a variable filter (Krohn Hite 3202r), which can do high pass, low pass, bandpass, and notch modes with a continuously variable corner/center frequency. It can be entertaining to set up the scope to display the frequency response in real time while playing with the filters.

p.s. MrW0lf, confine your FFT to a single period and you'll get the nice flat-top result. In this case, you want the DC imbalance that is present in the impulse response.