Fourier series : A FORMULAE that changed everything

Fourier series is a series which is used in DIGITAL SIGNAL PROCESSING a lot and apart from that if you are into signal and systems or any other geeky electrical and electronic subjects then you have to go through Fourier series, i mean let me tell you Fourier series is the real game changer, the formula can appear bit daunting but as a matter of fact it is pretty neat formulae to just distribute or let say visualize any function via sin and cosine,

i mean whatever input you have , put it in a Fourier system and it will find the sin and cos component of that function, i mean converting a signal from time domain to frequency domain and vise versa is what Fourier series is capable of.

I am a engineer and throughout my engineering Fourier series has been a very important part of my curriculum, i mean all the time we have to use either the Fourier series or the Fourier transform to find out a function output and i mean during my engineering days i was kinda confused what the heck it is but now it is quite clear to me how to use it and what to use it for.

Fourier series can be used for periodic function by this i mean if you have a non periodic function then you have to use Fourier transform , anyways if you using signals then anyways you will process them through a Fourier transform just to bring them down in the right format. You can choose the time format or the frequency format of the signal and with the help of Fourier series or even Fourier transform we can bring back the same signal and can interpret it in FREQUENCY or TIME DOMAIN.

Fourier series is a representation of a periodic function which can be equated as the sum of sine and cosine functions. I mean if you are going through Fourier series then also go through Taylor series which represents functions as infinite sums of monomial terms, it kinda helps to have a better understanding.

Anyways the Fourier series will have few important components and that components are the SIN and the COS component, plus the SIN and the COS component will have a Coefficient attached to em and you have to find the value of these coefficients which is not tricky because there is a simple formula for them aswell, along with this there will be a third coefficient as well in the beginning of the equation which can be calculated just by using another formulae.

The point to note here is that, there are kinda four formulae which is required to actually calculate the value of the Fourier series but you will find high level of symmetry in these formulae, i mean all of them are kinda similar, and as i am kinda done with words i am gonna share all the formulae that are important to calculate it.

Here is the formulae and some question related to Fourier series check em out :

Now once you are done with checking out the formulae then do check out these videos because after going through all this content you will finally be able to use Fourier series in real life scenarios.

NOTE : Fourier series is for periodic function and for non periodic function we use Fourier transform.

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