# Find the Fourier Transform

1. Sep 8, 2007

### bodensee9

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

I am supposed to find the Fourier Transform of the following:

suppose t(subu) is a translation of the function f by u, so that f*t(subu) = f(t-u).
suppose also that 1 means denotes a characteristic function so that the characteristic function has the value 1 from -T to T and 0 everywhere else.

1. f=t(subu)*1.

Would I evaluate the Fourier Transform with f = 1 from (-T+u) to T. My reasoning would be that since 1 means that f has value from -T to T, but then f is translated by u, so that you would need to add u to -T for f to have a value?

2. suppose that H is the heaviside function that takes the value of 1 from 0 to inf.

f = t(subu)*1*H.

would I evaluate the Fourier Transform from u to T? My reasoning is that because of H, f can only have a value from 0 to inf, but that is shifted by u, so you need to evaluate it from u to inf.

3. f = 1*t(subu)*H

would I get the same answer as 2?

Thanks very much.

2. Relevant equations

3. The attempt at a solution