[HN Gopher] An Interactive Guide to the Fourier Transform
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       An Interactive Guide to the Fourier Transform
        
       Author : pykello
       Score  : 111 points
       Date   : 2025-12-02 06:50 UTC (5 days ago)
        
 (HTM) web link (betterexplained.com)
 (TXT) w3m dump (betterexplained.com)
        
       | analog31 wrote:
       | My only quibble is that the article is about the _discrete_
       | Fourier transform.
        
         | shash wrote:
         | It's usually easier to explain the dft. and easier to do a
         | periodic function than a totally arbitrary sequence.
        
       | kuharich wrote:
       | Past comments: https://news.ycombinator.com/item?id=38652794
        
       | constantcrying wrote:
       | >The Fourier Transform is one of deepest insights ever made.
       | 
       | No, it is not. In fact it is quite a superficial example of a
       | much deeper theory, behind functions, their approximations and
       | their representations.
        
         | fedsocpuppet wrote:
         | The Fourier transform predates functional analysis by a
         | century. I don't see the point in downplaying its significance
         | just because 'duh it's simply a unitary linear operator on L2'.
        
           | NewsaHackO wrote:
           | But is it the deepest insights ever made?
        
             | badlibrarian wrote:
             | The Fourier Transform isn't even Fourier's deepest insight.
             | Unless we're now ranking scientific discoveries based on
             | whether or not they get a post every weekend on HN.
             | 
             | The FFT is nifty but that's FINO. The Google boys also had
             | a few O(N^2) to O(N log N) moments. Those seemed to move
             | the needle a bit as well.
             | 
             | But even if we restrict to "things that made Nano Banana
             | Pro possible" Shannon and Turing leapfrog Fourier.
        
               | lispisok wrote:
               | >Unless we're now ranking scientific discoveries based on
               | whether or not they get a post every weekend on HN.
               | 
               | Glad I'm not the only one who noticed there is a weekly
               | (or more) post on what Fourier transform is.
        
       | zkmon wrote:
       | It is more about the duality between the amplitude and frequency
       | spaces and conversion between them. A bit similar to Hadamard
       | gate for transforming a quantum state from computational basis to
       | diagonal basis.
        
       | kens wrote:
       | If you're dealing with computer graphics, audio, or data
       | analysis, I highly recommend learning Fourier transforms, because
       | they explain a whole lot of things that are otherwise mysterious.
        
       | biophysboy wrote:
       | My favorite application of the Fourier transform is converting
       | convolution into pointwise multiplication. This is used to speed
       | up multiple sequence alignment in bioinformatics.
        
       | seam_carver wrote:
       | If anyone wants to learn about the 2D DFT, the best explanation
       | I've ever read was the relevant chapter in Digital Image
       | Processing by Nick Efford.
       | 
       | If anyone wants to see my favorite application of the 2D DFT, I
       | made a video of how the DFT is used to remove rainbows in manga
       | on Kaleido 3 color eink on Kobo Colour:
       | 
       | https://youtu.be/Dw2HTJCGMhw?si=J6dUYOj2IRX1nPRF
        
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