# Fourier Series

Joined May 19, 2013
214
Consider the following article:
https://en.wikipedia.org/wiki/Fourier_series

At definition, they say that an = An*sin() and bn = An*cos()

So with these notations you can go from a sum having sin and cos to a sum having only sin but with initial phases.

Why can I write an = An*sin() and bn = An*cos() ?
It seems out of the blue.

Joined May 19, 2013
214
I figured it out. It follows from Pythagora's theorem in a right angle triangle.

#### Motanache

Joined Mar 2, 2015
523
It is not that difficult.
Look at this figure:

In the first image we have square signal.

LC oscillate as Sin():
https://en.wikipedia.org/wiki/RLC_circuit

So in the first image signal approaches with Sin() drew orange.

Last edited:

#### Motanache

Joined Mar 2, 2015
523
It is the main component of which will receive a radio, if you give a rectangular signal as in the first image.

In fact, RLC react to a growth rate (di/dt):

And the margins are 'very steep', that means I had very high frequency component.
So, what I could add up to that SIN ()(orange line) to drown the steep edges? corners.

This is the case sinusoids of blue and green.

Because we can not hatching the entire rectangle so, something must also substracted. Therefore we have cosine.

Last edited:

#### Motanache

Joined Mar 2, 2015
523
Forming a rectangular signal from sine signal: