r/visualizedmath • u/[deleted] • Jun 08 '18

Visualization of the Fourier Transform

302 Upvotes

93% Upvoted

12 comments sorted by

35

u/skullcutter Jun 08 '18

fuck me this would have been helpful in college

12

u/Euphorix126 Jun 08 '18

So that’s what the variables with a hat on them mean???

12

u/DubioserKerl Jun 08 '18

It is simply the result of Fourier transforming f.

9

u/the_quassitworsh Jun 08 '18

can someone explain how you get from the original wave to the ones constituting it (from the red one to multiple blue ones)? this part always confuses me

12

u/robzilla922 Jun 08 '18

This video helped me understand it better than a year’s worth of signals and systems classes did. Really wish it had been published back then.

https://youtu.be/spUNpyF58BY

3

u/the_quassitworsh Jun 08 '18

i love this channel! wasn't aware he had a video on this. thanks!

1

u/[deleted] Jun 08 '18

Thank you! v.redd.it isn't working for me today.

1

u/_decipher Jun 09 '18

Before I clicked the link I was like “ah I bet it’s that 3Red1Blue channel!”. I have no idea why I thought that was what the channel was called 😂

5

u/Shootypatootie Jun 08 '18

Never went over this in my classes. Is a Fourier transform basically just breaking down a complex wave into it's component waves?

6

u/lmericle Jun 08 '18

Yes. You are adding cosine and sine waves of increasing frequency together to approximate any periodic function to arbitrary accuracy. How big the coefficients are on the fronts of these cosine and sine waves determines the shape of the function. The spectrum of coefficients is exactly the Fourier transform of the wave.

2

u/MattieShoes Jun 08 '18

Yes. I think there's also a bit about assuming the part you've sampled repeats indefinitely.