- #1
J6204
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Thread moved from the technical forums, so no Homework Template is shown
In the following question I need to find the Fourier cosine series of the triangular wave formed by extending the function f(x) as a periodic function of period 2
$$f(x) = \begin{cases}
1+x,& -1\leq x \leq 0\\
1-x, & 0\leq x \leq 1\\\end{cases}$$
I just have a few questions then I will be able to get started to execute this solution.
**Question 1** How do I extend the function f(x) as a periodic function of period 2?
**Question 2** The formulas for determing the cosine series are the following,
$$a_0 = \frac{2}{L} \int_0^L f(x) dx$$
$$a_n = \frac{2}{L} \int _0^L f(x) \cos \left(\frac{n\pi x}{L}\right) dx$$
$$f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} a_n \cos\left( \frac{n\pi x }{L} \right)$$
Once we have extended the function what will the value of L be?
$$f(x) = \begin{cases}
1+x,& -1\leq x \leq 0\\
1-x, & 0\leq x \leq 1\\\end{cases}$$
I just have a few questions then I will be able to get started to execute this solution.
**Question 1** How do I extend the function f(x) as a periodic function of period 2?
**Question 2** The formulas for determing the cosine series are the following,
$$a_0 = \frac{2}{L} \int_0^L f(x) dx$$
$$a_n = \frac{2}{L} \int _0^L f(x) \cos \left(\frac{n\pi x}{L}\right) dx$$
$$f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} a_n \cos\left( \frac{n\pi x }{L} \right)$$
Once we have extended the function what will the value of L be?