 |
The 12 Term Fourier Series of a square Wave Note that only the odd harmonics appear. |
||
| Amplitude | Frequency (rad/sec) | Phase (degrees) | |
| 1 | 1 | 0 | |
| 1/3 | 3 | 0 | |
| 1/5 | 5 | 0 | |
| 1/7 | 7 | 0 | |
| 1/9 | 9 | 0 | |
| 1/11 | 11 | 0 | |
There is overshoot at the discontinuities of the square wave. Add more odd harmonics, up to the 23rd :
 |
The 24 Term Fourier Series of a Square Wave | ||
| Amplitude | Frequency (rad/sec) | Phase (degrees) | |
| 1 | 1 | 0 | |
| 1/3 | 3 | 0 | |
| : | : | : | |
| 1/21 | 21 | 0 | |
| 1/23 | 23 | 0 | |
 |
The overshoot remains. Adding even more components shows that the overshoot does not decrease in amplitude. This overshoot is called the Gibbs Effect. It is caused by the nature of convergence of the Fourier series. |
Previous Page