broegger
Oct9-04, 09:49 AM
Hi!
I have to calculate the Fourier coefficients c_n = \frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)e^{-inx}dx and the Fourier series for the following function:
f(x)=
\begin{cases}
\frac{2}{\pi}x + 2 & \text{for } x\in \left[-\pi,-\pi/2\right]\\
-\frac{2}{\pi}x & \text{for } x\in \left[-\pi/2,\pi/2\right]\\
\frac{2}{\pi}x - 2 & \text{for } x\in \left[\pi/2,\pi\right]
\end{cases}
Since this function is odd the Fourier series should only contain \sin{x} (right?), but I keep getting a series containing both sine and cosine. Furthermore I'm having big trouble with the integrals; are there any "tricks" when doing such integrals?
I have to calculate the Fourier coefficients c_n = \frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)e^{-inx}dx and the Fourier series for the following function:
f(x)=
\begin{cases}
\frac{2}{\pi}x + 2 & \text{for } x\in \left[-\pi,-\pi/2\right]\\
-\frac{2}{\pi}x & \text{for } x\in \left[-\pi/2,\pi/2\right]\\
\frac{2}{\pi}x - 2 & \text{for } x\in \left[\pi/2,\pi\right]
\end{cases}
Since this function is odd the Fourier series should only contain \sin{x} (right?), but I keep getting a series containing both sine and cosine. Furthermore I'm having big trouble with the integrals; are there any "tricks" when doing such integrals?