# How to Verify if the Fourier Transform is correct

At the exam of Mathematics 3 I have to do an exercise about the Fourier Transform. For exemple, I have a certain $f(x)$, and i have to compute $$\mathscr{F}[f(x)]= \hat{f}(\omega)= \int_{-\infty}^{\infty} f(x) e^{i\omega x}dx$$

My question is: is it possible, without calculating the anti-transform, to see if I have done some errors with the calculations? I mean, is it possible, looking the result,to understand intuitively if is it correct? In fact I don't have the time to anti-trasform $\hat{f}(\omega)$ to get the initial $f(x)$.

• That's difficult. There are some checks that can be done, e.g. symmetry and probably how fast it decays, but they can only show if the transform is incorrect, not if it is correct. – md2perpe Dec 6 '17 at 16:44
• Thank you for the answer. My teacher said something like the order of infinitesimal of the fourier transform and the discontinuities of the original function. However, could you explain better what do you mean for simmetry and how fast it decays? – cicciofrank19 Dec 8 '17 at 11:29