# Why can Fourier series be used on a non-repetitive function?

I was just wondering why Fourier series can be used on the function in the linked image. This is since I thought the function had to repeat itself to use Fourier series on it. Or is it saying a period is from 0-5s and so it will repeat every 0-5s? like the 2nd graph i made?

I can find the answer easily just not sure why fourier series can be used? ## 1 Answer

Fourier series can be calculated for any signal in close section (from $T_0$ to $T_1$). In fact, I was taught that this is how Fourier series is defined.

But Fourier series is made up of ($T_0 - T_1$) cyclic functions, therefore, if you go beyond the original section you will just get repetitions as you displayed.

• Thanks and so if i go beyond 5 seconds it will be like the second graph, or the 1st graph? – I have no clue Apr 4 '17 at 8:41
• like the second. – Maximilian Matthé Apr 4 '17 at 8:46
• so the fourier series would repeat i understand but would s1(t) repeat aswell or would it stay the same as graph 1? – I have no clue Apr 4 '17 at 8:48
• The signal would repeat, the Fourier series will stay the same. – Cherny Apr 4 '17 at 8:53
• Oh ok so it would stay the same as the signals are repeating correct?I.e. the Fourier series is the same for the next repetition? – I have no clue Apr 4 '17 at 8:55