I have the following $2 \pi$-period function f: $$ f(x) = \left \{ \begin{array}{l l l} x: & 0 < x < 2 \pi \\ \pi: & x = 0 \end{array} \right.\\$$
I try to calculate the trigonometric polynomial $t_3(x)$ with supporting points $x_k = \frac{k \cdot \pi}{2}, \quad k=0,\dots, 3.$
Now i thought i have to use the discrete fourier-analysis. But what exactly are my $y_j$, which i need to calculate the coefficients $a_k$ and $b_k$?
I don't really understand how to calculate this. In university we just defined the Polynom in the complex numbers.
Thank you very very much, for your help.
It's a sawtooth wave. You can easily find it on the internet (e.g. with Google), giving on top of the list: Sawtooth wave (Wikipedia), Fourier Series--Sawtooth Wave (Wolfram MathWorld).