Fourier Transform visualization

[Anonymous No.9653892]

https://www.youtube.com/watch?v=spUNpyF58BY
watching this gave my life meaning. i was always bothered by having literally no intuitions on fourier transforms. maybe i'm just a brainlet, but this shit is awesome.

[Anonymous No.9653928]

Ok, now try understanding convolution (and cross-correlation and auto-correlation - yes, they are different things).

If you'll understand convolution you'll be set in anything concerning signals.

[Anonymous No.9653954]

>>9653928
i also have no intuition on convolution. i can't visualize it. i don't even know how why multiplying in the frequency domain corresponds to convolution in the time domain.
about the correlation thing - i just think about them as measures of similarity. i don't know what i have to *understand* about them. that said, it may be that i just know too little to know what i don't understant

[Anonymous No.9653964]

>>9653928
What's the problem?

[Anonymous No.9654026]

>>9653892
That's neat and all but how do I understand 4D fourier transformations of operators into momentum space?

[Anonymous No.9654041]

>>9653964
-is the second function always reversed?
-why isn't the second g in g*g reversed (rising hypotenuse instead of falling)

[Anonymous No.9654047]

>>9653892
Thx senpai, gud video

[Anonymous No.9654053]

>>9653928
Convolution is just the weighted average of a function around a point where the weights are given by the other function (up to scaling, true average if the other function has integral 1)
So if you take a big wide bump you're averaging stuff from far away into each point and your function gets smoothened out. If you take a sharp one, the function stays almost the same because the averages are close. If you take a skewed bump, your average will favor stuff to that side and your function will simultaneously smoothen out and shift.
This is why convolution by the dirac delta shifted by x is just evaluation at x. It takes only the average at the point you care about, and then gives you that "average".
You can understand correlation similarly, but that's not the best intuition to have given its uses.

[Anonymous No.9654102]

>>9653928
Autocorrelation is a special case of cross correlation, you fool

[Anonymous No.9655223]

>>9653892
this is one of the best channels on youtube hands down
I also really liked his video on taylor series expansion and region of convergence, two other topics where i was only executing algorithms on abstract symbols to get the A

[Anonymous No.9655330]

>>9653954
I find doing 2D convolution is much better for intuition.
t. CS grad focusing on image analysis

[Anonymous No.9655750]

>>9653892
It clicked better for me when I started looking at different waveforms in the frequency domain.