Originally Posted by

**craig** Calculate the Fourier Transform of $\displaystyle g(x)$, where:

$\displaystyle g(x) =

\begin{cases}

x & 0 \le x \le 1 \\

2-x & 1 \le x \le 2 \\

0 & \text{otherwise}

\end{cases}

$

The formula that I've got is the Fourier transform $\displaystyle \hat{f}(s)$ of a function $\displaystyle f(x)$ is a function defined by:

$\displaystyle \hat{f}(s) := \left\int^{\infty}_{-\infty}\right f(x) e^{-isx} dx$

My question is, how would I go about calculating the Fourier Transform for the above function? Which value of $\displaystyle f(x)$ would I use, and which limits?

Thanks in advance.