An Interactive Guide to the Fourier Transform (2012)

I've been thinking a lot about how to apply FFTs to neural networks, so this is timely; thank you. If you're looking for deeper explanations, I recommend "Practical Signal Processing": https://www.amazon.com/Practical-Signal-Processing-Mark-Owen... Many of the chapters are here: https://battle.shawwn.com/sdb/books/PSP/ but buy the book if you can afford to. In particular, Chapter 4's "untwisting" intuition is the best I've found: https://imgur.com/a/r7KvO60 Another way of phrasing it: You know that effect when a…

On thing that is often overlooked but should be emphasized is that the considered frequencies are fixed values while the phase shifts are continuous values. This creates tons of downstream problems If your underlying signal is at frequency that is not a harmonic of the sampling length, then you get "ringing" and it's completely unclear how to deal with it (something something Bessel functions) Actually using DFTs is a nightmare .. - If I have several dominant frequencies (not multiples…

I don’t like the casting of the frequency domain view as the ‘recipe’ and the time domain view as the ‘product’. The point of Fourier is that you can switch between these perspectives losslessly - they contain equivalent information. The ‘smoothie’ metaphor of ‘unmixing’ the smoothie to get the ingredients, and then blending it to get the smoothie back conjures the impression that Fourier transformation is some sort of entropy reversing process, which is misleading. A time domain function has…

Great article. I did Fourier Transforms in EE maths and could apply them but never properly understand them. Typical calculation versus understanding. The greatest graphic in this entire article is if you ask me: http://betterexplained.com/wp-content/uploads/images/Derived... If all mathematics was explained like this, many less eyeballs would have been gouged out of sockets.