# Fourier transform problem

1. Nov 28, 2008

### leopard

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

Let a function f on (-$$\infty$$, $$\infty$$) be defined as

f(x) = cos x, if |x|<1;
f(x) = 0, otherwise

Find the Fourier transform of f and then evaluate the integral

$$\int ^{\infty}_{\infty} \frac{sin 2w}{w} cosw dw$$

2. The attempt at a solution

I calculate the Fourier transform: $$\frac{1}{\sqrt{2 \pi}}(\frac{sin(1-w)}{1-w} + \frac{sin(1+w)}{1+w})$$