Question:
Determine the Fourier series for the full wave rectified sine wave:
![](https://static.wixstatic.com/media/20c892_6cd4b5b9559f46dca0cb88387070b137~mv2.png/v1/fill/w_781,h_65,al_c,q_85,enc_auto/20c892_6cd4b5b9559f46dca0cb88387070b137~mv2.png)
Answer:
Sketch the Function and work out the period (L):
![](https://static.wixstatic.com/media/20c892_812eed1961aa495bbd3d192d1fc6c018~mv2.png/v1/fill/w_797,h_355,al_c,q_85,enc_auto/20c892_812eed1961aa495bbd3d192d1fc6c018~mv2.png)
The graph has a period of L=4𝜋.
The function is symmetrical in the y-axis. Therefore it is an even function and will contain no sine functions.
It has a period 4𝜋 so we can use the formula for Fourier Series of periodic functions for any period with L = 4𝜋.
![](https://static.wixstatic.com/media/20c892_97a2e243c66a40b383bf6482691700fb~mv2.png/v1/fill/w_774,h_676,al_c,q_90,enc_auto/20c892_97a2e243c66a40b383bf6482691700fb~mv2.png)
![](https://static.wixstatic.com/media/20c892_97ff637a649e40ad978dc6a079026e0a~mv2.png/v1/fill/w_781,h_642,al_c,q_90,enc_auto/20c892_97ff637a649e40ad978dc6a079026e0a~mv2.png)
![](https://static.wixstatic.com/media/20c892_050ce56b00fe44cfaecf4ffaa036350e~mv2.png/v1/fill/w_785,h_677,al_c,q_90,enc_auto/20c892_050ce56b00fe44cfaecf4ffaa036350e~mv2.png)
![](https://static.wixstatic.com/media/20c892_f1e0a166fcab43f78762b072b11b105c~mv2.png/v1/fill/w_782,h_636,al_c,q_90,enc_auto/20c892_f1e0a166fcab43f78762b072b11b105c~mv2.png)
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