Can someone explain to me how the fourier series works?

functions can be represented as a series of trigonometric functions. It makes analyzing the functions' properties a lot easier

>>9070722
Virgin magic and the sacrifice of at least one potential female partner

>>9070722
i legit just watched a video on this and it helped
https://www.youtube.com/watch?v=r18Gi8lSkfM

basically if you have any questions about any math intuition this dude has a intuitive video on it

Any piecewise continuous function can be expressed as a (potentially infinite) series of sines and/or cosines. The catch is that the function must be periodic or be extended periodically beyond a finite domain (also you may need an infinite number of terms in the expansion). If the function is not periodic and is defined over an infinite domain, the series must be formally replaced by an integral, and you get the Fourier transform of the function.

>>9070722
Any repeating squiggly line can be sorta more squiggly around zero (cosine) or not zero (sine). It can also be sorta more positiver on one side than the other. So what you do is plug in the desired squiggly line's parameters and work your way down from the biggest squiggles (is it going up or down, broadly speaking? Does it top out around zero?) to the smallest

>>9070722
Square integrable real functions of a real variable have a coordinate representation with respect to a basis of integer multiple frequency trig functions.

>>9070765
My nigga Eugene. He is a library of knowledge this guy

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its the principle of linear superposition.

>>9072840
i watched that for fun with no real math background and was impressed. Production value is great, clear and concise explanation. I actually learned something without trying

>>9070765

needs more raytracing

>>9070765


Here is the prerequisite video:

https://www.youtube.com/watch?v=6HCz1tFqIcs

>>9072893
what did i just watch

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>>9070765
Eugene has legit autism

>>9072925
holy shit im watching that video right now

who said i couldnt jerk off and learn things at the same time?

>>9072945
That's literally the only way I can learn things

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>tfw senior year
>physics major
>still don't have a grasp on Fourier series, still haven't needed it
How screwed am I?

>>9073190
if you know how to use fft library in a c++ random gay code you are ok

>>9070765
>any waveform or function can be made by a series of sine waves
holy SHIT...how do you even go about proving this?

>>9073480

it's mainly implicit in the definition of a series.

cos and sin allow you to cover the spectrum possible oscillations, and their arguments allow you to approach the desired wave form. utilize that structure and develop a series, as the arguments in your series (not your sin/cos arguments) approaches infinity, the expression converges to the desired waveform