### Author Topic: Fourier Series (Sawtooth Approximation)  (Read 1423 times)

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#### @rt

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##### Fourier Series (Sawtooth Approximation)
« on: October 31, 2015, 11:56:36 am »
Hi Guys

Could someone explain why there are two different circular animations about YouTube for Fourier Series Sawtooth animation?

Here’s one example where every second circle is rotating clockwise:

Yet the Wikipedia example here is different:

Wouldn’t these be two entirely different formulas?
At the very least I think theta would alternate positive and negative for the first example only.
I put this in projects section because it is a software project. I have been making my own.
Cheers, Brek.

« Last Edit: October 31, 2015, 11:58:19 am by @rt »

#### T3sl4co1l

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##### Re: Fourier Series (Sawtooth Approximation)
« Reply #1 on: October 31, 2015, 12:20:16 pm »
Probably, because cos(-x) = cos(x)?  For even harmonics, the direction of rotation doesn't matter, because they always have the same vertical component relative to the rest.

Tim
Seven Transistor Labs, LLC
Electronic design, from concept to prototype.
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#### @rt

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##### Re: Fourier Series (Sawtooth Approximation)
« Reply #2 on: October 31, 2015, 12:30:39 pm »
Lol can we forget the whole thing and make this thread go away?

There must be an issue with my rotation.
When I reproduce the second animation, as the iterations get near 200 or so,
the sawtooth becomes as good resolution as infinite is going to get on a limited resolution screen.
I can explain and fix the jittery points (it’s because I’m only connecting every third sample).

When I reproduce the first one it’s great except there’s a little kink in the middle of the diagonal part of the wave.
That is not uploaded though... I’ll look into it again :O

Smf