Author Topic: Fourier Series, Visualized  (Read 127 times)

Fourier Series, Visualized
« on: September 10, 2020, 10:47:50 AM »

As a keyboardist I have always been fascinated by Additive Synthesis, the approximation of a periodic signal by adding sinewaves. We can see this in action as we start to add sinewaves to get a near square wave by the 4th term. Notice how the amplitude must diminish with each odd and "faster" harmonic. I wish I had visualizations like this when I was in school !!!

Offline Baruch

Re: Fourier Series, Visualized
« Reply #1 on: September 10, 2020, 11:05:03 AM »
Ptolemy's epicycles were an early version.  Copernicus' actual system, though heliocentric, had more epicycles than Ptolemy.  It was only with Kepler that this fact could be hidden, for awhile.  Only to be rediscovered in the heat equation studies of Fourier.
Ha’át’íísh baa naniná?
Azee’ ła’ish nanídį́į́h?
Táadoo ánít’iní.
What are you doing?
Are you taking any medications?
Don't do that.

Re: Fourier Series, Visualized
« Reply #2 on: September 10, 2020, 11:43:49 AM »
And then there is the ancient Greek Antikythera mechanism (that may be as old as 200BC) that just bypasses all the complex math to solve astronomical positioning :bravo2:

Offline Baruch

Re: Fourier Series, Visualized
« Reply #3 on: September 10, 2020, 01:01:03 PM »
And then there is the ancient Greek Antikythera mechanism (that may be as old as 200BC) that just bypasses all the complex math to solve astronomical positioning :bravo2:

Genius analog computer.  Devised by Archimedes?
Ha’át’íísh baa naniná?
Azee’ ła’ish nanídį́į́h?
Táadoo ánít’iní.
What are you doing?
Are you taking any medications?
Don't do that.