- #1
bizuputyi
- 42
- 1
Homework Statement
Sketch the waveform and develop its Fourier series.
[itex]
f(\omega t)=
\begin{cases}
0 & if & 0 \leq \omega t \leq \frac{π}{2} \\
V*sin(\omega t) & if & \frac{π}{2} \leq \omega t \leq π\\
0 & if & π \leq \omega t \leq \frac{3π}{2} \\
V*sin(\omega t) & if & \frac{3π}{2} \leq \omega t \leq 2π
\end{cases}
[/itex]
Homework Equations
The Attempt at a Solution
I drew two sketches, please see attachment, I'm wondering which one is correct.
Calculating coefficients with V=1 just to see what the F.S. should look like, I've got:
[itex] a_0=0 [/itex]
[itex] a_n=\frac{1}{π}\left(\frac{2*sin\frac{nπ}{2}(-n+sin\frac{nπ}{2})}{-1+n^2} \right) [/itex]
[itex] b_n=0 [/itex]
Now, if a0=0 that implies that the first sketch is correct. If bn=0 that means the function is even, well, none of my sketches is an even function, something is definitely wrong here. Also, I found even harmonics zero, so [itex] f(\omega t)=f(\omega t+π) [/itex] which is true for the second sketch.
What did I do wrong? Thank you for looking into that.
Attachments
Last edited: