What is the definition of quarter wave symmetry?
As far as I understand the following definition should be the right one (but I'm not sure):
- For an odd function $f(\pi-x)=f(x)$
- For an even function $f(\pi-x)=-f(x)$
Why am I asking this? I need to calculate the Fourier series of a periodic rectangular function with amplitude $I_d$ and period $2\pi$ defined as follows:
\begin{cases} I_d & \text{ if } \frac{\pi}{6} <x< \frac{5\pi}{6} \\ -I_d & \text{ if } \frac{7 \pi}{6} <x< \frac{11 \pi}{6} \\ 0 & \text{ if } 0<x< \frac{\pi}{6} \text{or} \frac{5\pi}{6} <x< \frac{7\pi}{6} \text{or} \frac{11\pi}{6} <x< 2\pi \end{cases}
and I would like to calculate it using both the fact that I know it shows an odd symmetry AND a quarter wave symmetry. I can calculate it assuming both conditions are true, but I'm not sure I understand and know the definition of quarter wave symmetry and what it practically means for an odd or for an even function.
Please try to bring order into my mind on this topic if you can. Thank you.