# Thread: Basic Fourier Series question

1. ## Basic Fourier Series question

In comparison to the rest of the question in this section this will hopefully be easier for someone, here goes.

Let $f$be a function with period 2, such that:

$f(x) = \left\{
\begin{array}{l l}
-1 & \quad -1 \leq x < 0\\
1 & \quad 0 \leq x < 1\\
\end{array} \right.$

Find the Fourier Series of $f$.

$f$ is an odd function so $a_0 = a_n = 0$, and we know that $b_n = 2 \int^1_0 f(x) \sin{\pi n x}$.

I'm just not sure what to put for the $f(x)$, would it be 1 or -1?

Cheers for the help

2. Originally Posted by craig
In comparison to the rest of the question in this section this will hopefully be easier for someone, here goes.

Let $f$be a function with period 2, such that:

$f(x) = \left\{
\begin{array}{l l}
-1 & \quad -1 \leq x < 0\\
1 & \quad 0 \leq x < 1\\
\end{array} \right.$

Find the Fourier Series of $f$.

$f$ is an odd function so $a_0 = a_n = 0$, and we know that $b_n = 2 \int^1_0 f(x) \sin{\pi n x}$.

I'm just not sure what to put for the $f(x)$, would it be 1 or -1?

Cheers for the help
The way you have written it it would need to be $1$

if you used the limits of integration

$2\int_{-1}^{0}f(x)\sin(\pi n x)dx$ then it would be $-1$

both integrals will give the same value.

3. Many thanks