Looking for Periodicity by Using the Fourier Transform

[2fipi]

Homework Statement

One has a function g(x) that has a periodic nature, but the period is unknown (the term 'period' is used a bit loosely). To be specific, the g(x) (i.e. a signal) appears to oscillate, but the displacement between each oscillation is unknown (nothing is known about whether the period is varying or constant). g(x) is defined for all real numbers.

When taking the Fourier Transform of g(x), what would you put as the bounds for the integral itself?

Homework Equations

Also: g(x) 'somewhat' mirrors the function xsin(x), incase that's of importance.

The Attempt at a Solution

I'm guessing you cannot put an actual period value (as you do not know it), nor can you put Lower Bound: -T/2, Upper Bound: T/2 and let the period stretch to infinity, because the signal does appear to oscillate and appears to be loosely periodic. Other then these two methods, I'm not familiar with how to define the bounds of the Fourier Transform of g(x).

I've been stuck on this problem for a while, and I can't seem to get past that one thing. Any help would be greatly appreciated.

 

[vela]

You're mixing up the Fourier series with the Fourier transform. The integral for the transform has limits from $-\infty$ to $+\infty$. If there is a strong periodic component in g(x), you'll see a spike in the Fourier transform's amplitude at that frequency.