The practical sigmnificance of the Fourier Series is the Representatión of a Arbitrary Function helped with two ortogonal functions what are very familiar (sine cosine)
This Representation can show us the frequecy components of a signal....it is very useful in some areas...for example the thrird harmonic component of the current is cause of distorsion and resonance...for this reason some transformers have a harmonic filter for separate this component
Fourier Series give us a Discrete number of frequency components...(Countable Group of)
Excuse me if don't understand some parts ...but english isn't my first language
Added after 14 minutes:
We use Fourier Series when analize Periodic functions
fourier series is the representation of any signal in sinusoidal form...it will give the hormonics of signal.therefore u can see the which type of hormonics r there in the signal.(i.e 3,5,7etc).
then which type of harmonics r harmful for ur ckt
u have to filter out.
Getting to understand perspective in the frequency domain
is extremely helpful.
Some problem can solve easily in the frequency domain.
A signal can be represent itself in a frequency, time domain, etc...
It is only a different angle view, looking at the same apple on the table.
You will get to see a different view, if you look from the top.
It helps you to understand signal in the frequency domain view.
Yes thats right.. Fourier series gives you the harmonics present in the signal.. The practical application is the Fourier transform, which helps you in translating the signal to freq domain. The result is the same.. You get the inherent components present in the signal.. Series is as such not v useful in practical life..