# Condition for existence of Fourier transform?

We can convert signal into frequency domain using Fourier transform. But I think we can't compute Fourier transform of any signal . Fourier transform also should have some limits.

This is the definition: $$\hat{f}(\xi) = \int_{-\infty}^\infty f(x)\ e^{- 2\pi i x \xi}\,dx,$$ for any real number $ξ$.
We assume $f(x)$ is an integrable function, Lebesgue-measurable on the real line, and satisfy: $$\int_{-\infty}^\infty |f(x)| \, dx < \infty.$$
• Well, maybe that's the beginning. But the Fourier transform can be defined for $f\in L^2$ and in the sense of distributions, for any locally integrable function, measures etc.