# Fourier transform - what integral limits

1. Mar 2, 2012

### zezima1

Find the fourier transform of the unit rectangular distribution f(t) = 1 for ltl<1 else 0
Since e-iωt is zero except for t in ]-1;1[ it must be an integral over this interval. But should I take the boundaries as -1 and 1? Because they are not included in the interval where e-iωt is not zero but rather supremum and infimum for it. Would it better to put the limits lim t->1 and lim t->-1?

2. Mar 2, 2012

### MathematicalPhysicist

What?
The exponent never vanishes for finite values.

3. Mar 2, 2012

### zezima1

umm the fourier transform is:

-∞f(t)e-iωtdt

But since f(t)=0 for t≥1, t≤-1 you integrate from -1 to 1?

4. Mar 2, 2012

Yes.

5. Mar 2, 2012

### vela

Staff Emeritus
I think you meant f(t) where you wrote e-iωt.

Regarding your question about the limits, it turns out it doesn't matter. You can look up some statement about the uniqueness of Fourier transforms. I think it's something like two functions have the same Fourier transform if they differ over a set of points of measure 0.