# Bandwidth and probability of continuous signal

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.

• Your function definition makes no sense; is it of if I replace the $x=$ with an $f(x)=$? – Marcus Müller Jan 5 at 12:35
• Probability distribution of what exactly? under which conditions? Also, you'd have to tell us how your material defines "bandwidth"; if you use the strict definition (based on the support in frequency domain), this has infinite bandwidth, no calculation needed, as it is finite in support in time. – Marcus Müller Jan 5 at 12:37
• (I very much presume your question is easy to answer – even for you – once you write down all assumptions that are relevant.) – Marcus Müller Jan 5 at 13:03
• i think this is a nonsensical question. it can't be answered factually. – robert bristow-johnson Jan 11 at 2:04

the function consists of six individual line segments. You probably should calculate the probability density function of each line segment, weigh them by $$1/6$$ and combine them into a single pdf. That will be easier if you draw it an stare at it for a bit.
• not agreeing with the second point: a function doesn't have a probability distribution, it's deterministic. What has a probability distribution is the value of the function if you applied the function to a random variable - but then Augustin would have to define the distribution of $x$ to even get something useful. Your assumption that $x$ is uniform on $[-3;3]$ falls out of the bluest of skies! – Marcus Müller Jan 5 at 12:52