1. Complex Fourier

hey

complex to say atleast.

im stuck with the exercise beneath. i have to work this out by monday but i need some help, i don't know integration by parts that well if that is what is used to work it out and i don't quite get how can i show it graphically. im hoping someone will cheer me up and solve this with me so i have an example for in the future.

f(t) = 0 for t ∈ [0,3]
f(t) = 3 for t ∈ [-3,0]

Period = 6

"Work out the function and plot 2 periods of the signal, also show it graphically for a series (5 terms)."

The answer of the function should look like this

thanks for the kind person(s) who are willing to help, it's really a blessing.

kind regards
kim

2. Originally Posted by Kimmeke
hey

complex to say atleast.

im stuck with the exercise beneath. i have to work this out by monday but i need some help, i don't know integration by parts that well if that is what is used to work it out and i don't quite get how can i show it graphically. im hoping someone will cheer me up and solve this with me so i have an example for in the future.

f(t) = 0 for t ∈ [0,3]
f(t) = 3 for t ∈ [-3,0]

Period = 6

"Work out the function and plot 2 periods of the signal, also show it graphically for a series (5 terms)."

The answer of the function should look like this

thanks for the kind person(s) who are willing to help, it's really a blessing.

kind regards
kim

$f(t) = \begin{cases}
3, & \mbox{if}~~- 3 \leqslant t \leqslant 0; \\
\end{cases}$

$f(t) = \frac{3i}{2\pi}\sum\limits_{n= -\infty}^{+\infty} \frac{1 - e^{i\pi n}}{n}e^{i\tfrac{\pi nt}{3}} = \frac{3}{2} - \frac{6}{\pi}\sum\limits_{n=1}^{+\infty} \frac{1}{2n - 1}\sin\frac{(2n - 1)\pi t}{3} .$

"Work out the function and plot 2 periods of the signal, also show it graphically for a series (5 terms)."
I think it should look that way:

Also see the attachment (higher quality).