What Do Fourier Series Actually Reveal About Signals?

[MartinV05]

I've just started learning Fourier series and I'm having trouble understanding it. What do they actually do? And what does the amplitude-frequency show me? I'm asking as a rookie in signal analysis, so if you could explain it to me as simple as you can it will be of great help.
Thanks!

 

[Pythagorean]

It's a way to measure many scales of your signal at once. If you can represent a function with a Fourier series, you can decompose the function into components, and each component can be characterized by an amplitude and frequency.

So if you have a signal with 60 Hz in it, you could decompose it into it's spectral components, subtract all components with a frequency near 60 Hz, then transform it back into a signal and the 60 Hz will have magically disappeared... along with any component of your signal that was 60 Hz (that's the sacrifice you make).

Or... if you have an unfamiliar set of signals, you could begin to characterize them by their chief frequencies.

 

[NascentOxygen]

I've just started learning Fourier series and I'm having trouble understanding it. What do they actually do? And what does the amplitude-frequency show me?

If you add a lot of sinusoids together, carefully adjusting the amplitude and frequency (and phase) of each, you can generate any shaped waveform you wish, triangle wave, rectangular wave, square wave with a blip on the rising edge, the waveshape of a heartbeat on an ECG, the electrical interference from a distant lightning bolt, etc., etc., any complex waveform you care to nominate.

The amplitude vs frequency list describes the sinusoids you need to achieve this feat.

 

[Pythagorean]

you can generate any shaped waveform you wish

That's not entirely true, of course; there are lots of places where it fails, but for most functions you can get a good approximation.

 

[MartinV05]

Ok guys, thank you so much. I think I got it!
Cheers