I'm a little bit confused as to how to calculate the bandwidth of a signal. A question has me believing that it is correlated with the probability distribution. I am however not sure of this.
Suppose you have the following function:
How exactly do you calculate the bandwidth?
I was thinking of doing a fourier transform, but that seems a little bit cumbersome. In this particular question, an engineering rule of thumb was mentioned so I was also thinking about the Nyquist theorem. But to apply that you have to determine a sampling frequency.
In this problem they also ask for a probability distribution so maybe it has something to do with that. I do, however, not know how to calculate said distribution.
Edit: Thanks for the replies. I cannot answer your comments so I will supply some extra information here: indeed the x should be f(x), that was a typo, my bad. The distribution of x is uniform. I would like to know how to calculate the distribution of f(x) (so p(f(x))). As for the bandwidth. I think infinite bandwidth is technically correct, but I think (this isn't given in the question though) that they really want to know the zero-to-zero bandwidth.