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The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?

Reducible · 2.3M views · 2020-11-14 · 28:23

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Overview

Reducible's visual walkthrough of the Fast Fourier Transform, motivated by polynomial multiplication. It shows how the FFT's key ideas can be discovered by asking the right questions.

On Hacker News

HN repeatedly calls it a fantastic explanation that made FFT click, with some rewatching it periodically.

Recommended by 7 HN people across 8 months · HN mentions 2021–2026

Topics

Algorithms & data structuresInformation theory & signal processing
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fftpolynomial multiplicationalgorithmsconvolutionsignal processing

What people said

tverbeure · 2025-10 · Strong recommendation

I almost always prefer text over video, but this video on the same subject is fantastic: [VIDEO] . I watch it at least once every year. Also, the title of the blog post (and by extension this HN post) is IMO not really correct: it's not about the DFT but specifically about the FFT.

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tverbeure · 2024-07 · Strong recommendation

If you haven’t seen it yet, you should watch this video: [VIDEO] It derives the FFT algorithm from polynomial multiplication and it’s fantastic . I rewatch it every 6 months or so.

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kippinitreal · 2023-01 · Strong recommendation

That video did the same for me. I also like the reducible video for Fast Fourier Transforms as well as the Veratasium piece that shares some fun history. Reducible - FFTs the most ingenious algorithm ever [VIDEO] Veritasium - The Most Important Algorithm of All Time [LINK]

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Sources

Video by Reducible, played through YouTube.

Data and selection notes

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HN Library: HackerTube export (2026-10-31) and open-index/hacker-news. Upstream summaries and classifications may contain AI errors.

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