Need knowledge about bandwith in DSO

[Galli]

Hello, I'm currently doing my technician. I have a question about the following task.

"What minimum sampling frequency must a DSO have in order to be able to measure the fall time in the pulse voltage shown in Fig. 1.1 up to the 9th harmonic using dot reproduction, vector interpolation and sine interpolation?"

The frequenz of this pulse is not essential, i will understand the theory behind this.

I know the Nyquist theorem, which says: bandwidth > f*2

So far so good. I bought the solution to this task online because I want to check my solution afterwards to get my grade.
Unfortunately, I couldn't find anything when I searched online and in my study documents as well
I want to understand the topic and not simply write it off.

 The solution to the task was as follows:
Bandwidth for sine interpolation (si(x)) = f*2.5 (Nyquist okay)

but for the bandwidth
Vector interpolation = f *10
and for dot reproduction = f*25

I wonder where the other two factors come from and why I can't just use one factor for all 3 functions?
And why exactly these factors? And not, for example, *30 or *50. Is there any practical experience here?

Thank you for help

[ataradov]

Apart from Nyquist, those are just arbitrary numbers. I assume  they are matching whatever course material was given.

There is no Fig 1.1 attached. But you need to keep in mind that "f" here would be the frequency of the highest harmonic you want to reproduce. For a pure sine wave it would be the frequency of that sine wave. For anything that is not sine, you have to take harmonics into account or you will be restoring sine waves.

Sampling rate 10x of the signal frequency is an often used rue of thumb when observing digital signals. This is the point where square things still look square.

And the only reason for dot reproduction to be higher is to increase the density of the dots. It is no different that vector interpolation and if you can imagine lines between the dots, you don't need 25x sampling.

[Galli]

Only "random" numbers, okay, and in the practice the factor ten is used normally.

 

Thank you, ataradov.