File this under fourier analysis **+** linear algebra **=** bad#ss.

**Fourier transform of toes**

On the right you’re seeing the *configuration space* of the toes as opposed to physical space of the toes.

**Ponies**

Take a 3-D mesh wireframe stallion and do the Fourier transform.

Now you have a summary of the position, so you can move hoof-leg-and-shoulder by just moving 1 point in the transformed space.

In other words the DFT takes you into the *configuration space* of the horsie. Inverse DFT takes a leg-and-hoof configuration and gives you back a wireframe horsie.

**clustering**

The discrete Fourier transform also helps sort out the clustering problem:

**smoothing**

From the slides, I don’t get what the connection is to (anti-fractal) smoothing. But…seahorses and seagulls:

PDF SLIDES via Artemy Kolchinsky

If you thought linear regression was a hammer for every nail … wait until you play around with the Fourier transform!

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Tags: DFT, discrete Fourier transform, Fourier analysis, linear algebra, mathematics

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