The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever? on HackerTube: recommended by 7 Hacker News commenters across 8 separate months, 2021–2026.
explainer · intermediate · evergreen
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.
HN repeatedly calls it a fantastic explanation that made FFT click, with some rewatching it periodically.
“It derives the FFT algorithm from polynomial multiplication and it’s fantastic . I rewatch it every 6 months or so.”
9 Hacker News comments link this video. Each one links back to its thread.
I almost always prefer text over video, but this video on the same subject is fantastic: ▶ this 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.
in “Discrete Fourier Transform” · View on HN
If you haven’t seen it yet, you should watch this video: ▶ this video It derives the FFT algorithm from polynomial multiplication and it’s fantastic . I rewatch it every 6 months or so.
in “Convolutions, Fast Fourier Transform and polynomials (2022)” · View on HN
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 ▶ this video Veritasium - The Most Important Algorithm of All Time [link]
in “Ask HN: Concepts that clicked only years after you first encountered them?” · View on HN
As the author mentions, convolutions for signal processing and convolutions for probability are essentially equivalent things in two different contexts. It is interesting that the same concept is behind the multiplication of polynomials. In the discrete case we have the parallel of the vectors representing ... the (discretized) probability density <-> the (discrete) signal intensity <-> the coefficients of the polynomial ... in the respective context. If we look at the discrete case, since the operation of convolution is computationally expensive (O(n^3)), people often rely on the Fast Fourier Transform Algorithm (FFT), that runs in O(n log(n)). An excellent and very enjoyable video on the FFT applied to the polynomial multiplication is ▶ this video .
in “Understanding Convolutions in Probability: A Mad-Science Perspective” · View on HN
Not a book, but I truly enjoy this guy’s videos: ▶ this video . I usually watch them while eating lunch. He does a truly fantastic job.
in “Ask HN: Most interesting, mildly impractical, well-written books on software?” · View on HN
For anyone interested and with 30 minutes to spare, I would recommend the youtube video [1] by Reducible for an intuition on how FFT works. [1]: ▶ this video
in “Understanding the FFT Algorithm (2013)” · View on HN
Related: Fast Fourier Transform (FFT) can be used for polynomial interpolation in O(nlogn) time (if you get to choose the points, and use “complex roots of unity”), where n is the degree of the polynomial, and is used as a step in multiplication of polynomials in O(nlogn) as well. This video covers it well: ▶ this video Also, chapter 30 of CLRS: [link]
in “Polynomial Interpolation” · View on HN
And an FFT explanation by Reducible - ▶ this video It's in a similar style to 3blue1brown (uses the same visualisation library) but the video focuses specifically on the FFT algorithm, not on Fourier transforms in general. I'm pretty sure Grant himself recommended the Reducible video at some point.
in “A gentle introduction to the FFT (2002)” · View on HN
Were you watching this video by any chance? ▶ this video ("The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?" by Reducible)
in “The Focus to Say No (2011)” · View on HN