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I have a pretty simple question I think, but I cannot really find satisfying solution. The question is from an old examination sheet. The question is: "What do you have to consider when you want to produce a signal with steep edges, e.g. a nearly rectangular pulse, concerning the bandwidth of the spectrometer? And why do you have to consider it?" I translated the question by myself into english, so please ask if something is not clear.

My idea was to look on the Fourier transform of a rectangular pulse, which is a sinc-function depending on the frequency, but I have problems to connect it to the bandwidth of the spectrometer or to understand how this can help me with the procedure of producing signals with steep edges.

I would be really happy to have some input from you guys! Thanks in advance!

UPDATE:

Thanks for your reply. My thoughts were just that the spectrum of the rectangular pulse is a sinc-function and that the effective excitation is between the first two roots (positive and "negative" frequency). Therefore, I have to ensure that the spectrometer has a bandwidth of at least the distance between these two roots, so that it can be indeed "used" by the spectrometer since it is only measuring the frequency content of a signal. But then, when I have a triangular pulse, which has a sinc^2-function as the spectrum, it follows that the reasonable bandwidth should be also between the same roots but this signal does not have such steep edges as the rectangular pulse. Therefore, I cannot really find a reason of how to choose the bandwidth of the spectrometer if I want to ignore facts as sampling rate etc., when I have signals with steep edges as a rectangular pulse.

This is a more conceptual question, which wants to connect the bandwidth of the spectrum of the actual signal with the bandwidth of the spectrometer.

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Regarding producing the signal with steep edges you have two practical limitations.

  1. Slew-rate, i.e. the maximum rate of change
  2. The bandwidth, the maximum single tone frequency.

Both are physically teid to the same parameters.

The spectrometer is a device that measures the frequency content of a signal. These instruments, as all others, also has bandwidth limitations, so you cannot measure steeper edges with the spectrometer than it's bandwidth allows.
A spectrometer with a bandwidth of 10 GHz will be able to measure edge steepness around 1 V/100 ps.
Depending on whether you use an analog or digital spectrometer the bandwidth limit will typically be set by the input impedance or the sample rate.

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