# Fourier Transform - convolution theorem

I have been studying the Fourier Transform and the convolution theorem is not clear to me.

Sometimes, I see this:

But other times I see this:

Which one is correct? Where is this constant factor from?

• These two different definitions. You should make sure which one you are working with. Commented Jul 26, 2017 at 17:14
• And how do I know which one I am working with? I mean, what is the source of the difference between these two? Commented Jul 26, 2017 at 17:19
• You know there are different ways to define the F.T., right? They are different because of a factor of $1/2\pi$ in either the forward or inverse FT, or possibly a factor of $1/\sqrt{2\pi}$ included in each. You need to know which definition of the F.T. and I.F.T. your source is using. Commented Jul 26, 2017 at 17:21
• It's about the convention. The definitions are usually communicated before the usage. Take a look physicsforums.com/threads/… Commented Jul 26, 2017 at 17:21
• I didn't know about the other definition, thank you!! Commented Jul 26, 2017 at 17:24

## 1 Answer

Thanks to @ThePhoton and @EugeneSh., it turns out there are different definitions of Fourier Transforms.

https://www.physicsforums.com/threads/why-the-1-sqrt-2-pi-in-the-definition-of-the-fourier-transform.487312/