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

Reducible · explainer · Watch on YouTube

Algorithms & data structuresInformation theory & signal processing

What it is

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.

Why Hacker News recommends it

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

  • 7 people recommended it
  • 8 different months
  • 5 strong recommendations
  • first 2021, last 2026

What HN commenters said

  1. “I truly enjoy this guy’s videos”

    withinboredom, 2021-11 · Strong recommendation · in “Ask HN: Most interesting, mildly impractical, well-written books on software?”

  2. “An excellent and very enjoyable video on the FFT applied to the polynomial multiplication is”

    FFT applied to polynomial multiplication

    squaredot, 2022-12 · Strong recommendation · in “Understanding Convolutions in Probability: A Mad-Science Perspective”

  3. “That video did the same for me.”

    Made FFT concepts click

    kippinitreal, 2023-01 · Strong recommendation · in “Ask HN: Concepts that clicked only years after you first encountered them?”

  4. “It derives the FFT algorithm from polynomial multiplication and it’s fantastic . I rewatch it every 6 months or so.”

    Derives FFT from polynomial multiplication

    tverbeure, 2024-07 · Strong recommendation · in “Convolutions, Fast Fourier Transform and polynomials (2022)”

  5. “the video focuses specifically on the FFT algorithm, not on Fourier transforms in general.”

    FFT explainer in 3blue1brown style, focused on the algorithm

    jstx1, 2021-10 · Recommendation · in “A gentle introduction to the FFT (2002)”

  6. “This video covers it well”

    Covers FFT for polynomial interpolation and multiplication

    foooobaba, 2023-02 · Recommendation · in “Polynomial Interpolation”

  7. “I would recommend the youtube video [1] by Reducible for an intuition on how FFT works.”

    Intuition for how FFT works in 30 minutes

    medbar, 2026-04 · Recommendation · in “Understanding the FFT Algorithm (2013)”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: fft, polynomial multiplication, algorithms, convolution, signal processing

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