# Thread: Is the sum of two fourier series also a fourier series?

1. ## Is the sum of two fourier series also a fourier series?

yeah so is the sum of two fourier series also a fourier series? I am given two fourier series and told to find the fourier series of a combination of the two and I am wondering if i can simply combine the two?

2. Originally Posted by hmmmm
yeah so is the sum of two fourier series also a fourier series? I am given two fourier series and told to find the fourier series of a combination of the two and I am wondering if i can simply combine the two?
That if true only if the periods of the two functions satisfy the relation...

$\displaystyle \frac{T_{1}}{T_{2}} = \frac{m}{n}$

... where $m \in \mathbb{N}$ and $n \in \mathbb{N}$...

Kind regards

$\chi$ $\sigma$

3. so that the ratio of the periods of the two functions is rational? Is this because the sum of two periodic functions is only periodic if the ratio of their periods is rational?