# Duality and Fourier Transform

1. Nov 15, 2011

### c299792458

1. The problem statement, all variables and given/known data
How do I use the $(FF(f))(x)=2\pi f(-x)$ where $F$ is the Fourier transform.
and $F(f(x-a))(k)=\exp(-ika) X(k)$ where $X(k)=F(f(x))$

to get $F(\exp(iax)f(x))(k)=X(k-a)$

2. Relevant equations