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Seeing an epicycles animation years ago did wonders for my understanding of the complex representation of Fourier series, and I’ve been looking for that animati
by szvsw 2y ago
Seeing an epicycles animation years ago did wonders for my understanding of the complex representation of Fourier series, and I’ve been looking for that animation ever since to share with others getting into signals for the first time. This post far surpasses that page though! Excellent work, excited to share it with people in the future.
- Koshkin 2y agoThere's quite a few of those out there, e.g. https://youtu.be/k8FXF1KjzY0 https://youtu.be/k8FXF1KjzY0.
- chuckadams 2y agoMy favorite is https://youtu.be/n-43Uje-OuQ https://youtu.be/n-43Uje-OuQ
- westurner 2y ago"The more general uncertainty principle, regarding Fourier transforms" by 3blue1brown https://youtube.com/watch?v=MBnnXbOM5S4 https://youtube.com/watch?v=MBnnXbOM5S4 From https://news.ycombinator.com/item?id=25190770#25194040 https://news.ycombinator.com/item?id=25190770#25194040 : > Convolution is in fact multiplication in Fourier space (this is the convolution theorem [1]) which says that Fourier transforms convert convolutions to products. 1. https://en.wikipedia.org/wiki/Convolution_theorem https://en.wikipedia.org/wiki/Convolution_theorem : >> In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms. "QFT and iQFT; Inverted Quantum Fourier Transform" https://en.wikipedia.org/wiki/Quantum_Fourier_transform https://en.wikipedia.org/wiki/Quantum_Fourier_transform