# Fourier transform

1. Feb 25, 2012

### homad2000

1. The problem statement, all variables and given/known data

if y(ω) = F{x(t)}, what is F{y(t)} (F is the fourier transform operation)

2. Relevant equations

non

3. The attempt at a solution

I tried finding F^-1{y(ω)}, which is equal too x(t), but I could not go on with finding F{y(t)}

2. Feb 25, 2012

### I like Serena

Hi homad2000!

Check the section on "duality" on the wiki page: http://en.wikipedia.org/wiki/Fourier_transform
It says what the transform is of a transform with the domain swapped.

3. Feb 25, 2012

### homad2000

Ok, correct me if I'm wrong:

I got F{y(t)} = x(-ω) ? or should I add the 2π to that?

4. Feb 25, 2012

### I like Serena

Yep. That's it.

Whether or not 2π should be added depends on the definition of your Fourier transform.
As you can see on the wiki page, there are 3 different common definitions.
Which of the 3 does your text book use?

5. Feb 25, 2012

### homad2000

I believe i should add the 2 pi, because we use w = 2 * pi * f

Thank you for your help, I appreciate it :)

6. Feb 25, 2012

### I like Serena

That would not be the reason.

Your Fourier transform would be defined as either:
$$F(\omega)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} f(t) e^{-i \omega t}\, dt$$
or
$$F(\omega)=\int_{-\infty}^{\infty} f(t) e^{-i \omega t}\, dt$$

In the first case you would not have a factor 2pi, while in the second case you would have a factor 2pi.

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