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Shannon's theorem tells us the minimum sampling frequency based on the bandwidth of the signal which has to be sampled.
But I wonder, how can I know the signal's bandwidth before sampling it?
It is generally assumed that one knows in advance the continuous time dependence of the signal (that is, f(t)), but I don't understand how this information can be available without a measurement, which in turn requires a sampling rate to be chosen.
It depends on the purpose of the sampling.
If you need to sample a signal accurately - such as recording music where distortion is undesirable, you know the signal's bandwidth at the ADC, because you already ran it through a low pass filter.
This also works with slices of bandwidth above the Nyquist frequency or even above the sample rate, provided the slice has been selected via a narrowband filter. For example the output of a narrow 10.7 MHz IF filter may be sampled at 10 MHz, and will appear as signals around 0.7 MHz. This is known as undersampling.
If you need to detect any signal activity but you're most interested in the presence or absence of signals, or the envelope, or total energy, so that accuracy is less important, then just sample the signal, and be aware that aliasing introduces ambiguity in the frequency of any components.
Comparing two sampled channels, one via a low pass filter and one without, will alert you to activity outside the Nyquist frequency rate; if you need to do something about that, then you can take further steps (such as, bandpass filters ahead of the ADC to identify which spectral image is active, or changing the sample rate).
This is where engineering judgment and/or experience plays a role. The definition of "sampling at a super-high rate" can mean different things for different people or applications. There are also cost and feasibility tradeoffs to consider as well. The engineering part comes in where you have to evaluate what you think the type of bandwidth may be and then give that a go. Research into unknown things very often takes trial and error methods and successive refinement of your process.
All possible phenomena that you can measure have a maximum bandwidth, if nothing else the recording device (microphone, photodiode, etc) is a low pass filter. You can always look at the specs of your measurement device and sample sufficiently to cover it's bandwidth.
Before sampling you will have to run it trough a low pass filter in order to prevent aliasing.
You should not sample a signal with higher frequency components then you can sample. Since you'd have no clue what you have sampled and how to reproduce or present it.
If you do not know the bandwidth of the source, then what you trying to sample anyway?
If you want a communication system with acceptable bit-error-rate, then you need to include enough energy to provide a healthy (well opened) data eye.
If the system has massive error-correction, then some of that previously-required higher-frequency energy has become optional.
Thus you might use BIT ERROR RATE as indicator of when your system has enough bandwidth.
