3blue1brown but what is a convolution

Загружено автоматически через бота оригинал 3blue1brown оригинальное описание
discrete convolutions from probability to image processing and ffts.
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other videos i referenced
live lecture on image convolutions for the mit julia lab
on discrete fourier transforms
video on ffts
video on ffts
small correction for the integer multiplication algorithm mentioned at the end. a straightforward application of fft results in a runtime of on logn loglogn . that loglogn term is tiny but it is only recently in 2019 harvey and van der hoeven found an algorithm that removed that loglogn term.
another small correction at 1700. i describe on
2 as meaning the number of operations needed scales with n
2. however this is technically what thetan
2 would mean. on
2 would mean that the number of operations needed is at most constant times n
2 in particular it includes algorithms whose runtimes dont actually have any n
2 term but which are bounded by it. the distinction doesnt matter in this case since there is an explicit n
2 term.
these animations are largely made using a custom python library manim. see the faq comments here
can find code for specific videos and projects here
by vincent rubinetti.
the music on bandcamp
p.comalbumthemusicof3blue1brown
stream the music on spotify
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timestamps
000 where do convolutions show up
207 add two random variables
628 a simple example
725 moving averages
832 image processing
1342 measuring runtime
1440 polynomial multiplication
1810 speeding up with ffts
2122 concluding thoughts
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