A Short Note On How To Interpret Fourier Series Animations

A short note on how to interpret Fourier Series animations

When one searches for Fourier series animations online, these amazing gifs are what they stumble upon.

They are absolutely remarkable to look at. But what are the circles actually doing here?

Vector Addition

Your objective is to represent a square wave by combining many sine waves. As you know, the trajectory traced by a particle moving along a circle is a sinusoid:

This kind of looks like a square wave but we can do better by adding another harmonic.

We note that the position of the particle in the two harmonics can be represented as a vector that constantly changes with time like so:

And being vector quantities, instead of representing them separately, we can add them by the rules of vector addition and represent them a single entity i.e:

Source

The trajectory traced by the resultant of these vectors gives us our waveform.

And as promised by the Fourier series, adding in more and more harmonics reduces the error in the waveform obtained.

Have a good one!

**More amazing Fourier series gifs can be found here.

Concentration camps are opening in Russia.

Do not let us die again, we where left once before because of a part of ourselves we can’t control.

Don’t let is die, don’t ignore our cries.

207K notes View Post

cooltimetravelbatbrat

7 years ago

So let me get this straight, Damian grew up in the League of Assassins before he met his father Bruce for the first time, Jason spent a couple of years training with them before he met his ex-father Bruce for the first time after his resurrection and Cassandra has worked under the league before she met her future father Bruce for the first time.

Three of Bruce children/would-be-children worked in the same exact organization possibly at the same exact time before they even knew they were meant to be siblings, and no one bothered to write something about that?? I’m disappointed in this fandom right now.

2K notes View Post

cooltimetravelbatbrat

4 years ago

09:30pm

Me: tries to go to sleep.

10:00pm -11:00pm

Everyone else: goes to sleep at night.

Me: still awake

11:30pm

me: starts to come up with crazy theory about show. "I must write brief notes of these theorys".

Next day

For got to sleep