# Fourier Transform

1. Jan 28, 2010

### phrygian

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

f(x) = {-1, -pi<x<0 ; 1, 0<x<pi ; 0, |x|>pi}

Find the exponential Fourier transform of the given f(x) and write f(x) as a Fourier integral.

2. Relevant equations

3. The attempt at a solution

I have the equations for the Fourier transforms and I know how to find the Fourier series for f(x) but I have no idea where to start this one, my book is very confusing. Can someone help me start this?

2. Jan 28, 2010

### vela

Staff Emeritus
What is the definition of the Fourier transform you are using?

3. Jan 28, 2010

### HallsofIvy

The Fourier transform I am familar with is
$$\frac{1}{\sqrt{2\pi}}\int_{x=-\infty}^\infty f(x)e^{-isx}dx$$
If that is what you know, just go ahead and do the integration:
$$\frac{1}{\sqrt{2\pi}}\left(-\int_{-\pi}^0 e^{-isx}dx+ \int_0^\pi e^{-isx}dx\right)$$