3 ms·
Perhaps interestingly this visualisation technically depicts only half of the Fourier transform. The full transform adds the exact mirror image of each circle t
by contravariant 5y ago
Perhaps interestingly this visualisation technically depicts only half of the Fourier transform. The full transform adds the exact mirror image of each circle to cancel out the horizontal movement (which is usually drawn vertically, but this visualization swaps the real and imaginary axes).
This means that what this visualisation effectively depicts is the analytical signal [1] which is what you get when you use the hilbert transform to 'recover' the imaginary part of the original signal. This transformation is convenient as it allows you to determine the instantaneous phase and amplitude at each point in time, so you can calculate a frequency and volume for every single moment in time.
[1]: https://en.wikipedia.org/wiki/Analytic_signal https://en.wikipedia.org/wiki/Analytic_signal
- jimmySixDOF 5y agoId like to see what this would look like in a 3D model visualization similar to what 3blue1brown produce. These graphics communicate math so much better and are the perfect fit for AR/VR.
- nitrogen 5y agoBy sheer coincidence, I've been working on a couple of videos that explain analytic signals using 3D animations from my own animation engine, and why they're useful. I hope to upload the first one in the next week. A link to my channel is in my HN profile, if you're interested in the earlier videos in the series.
- jay3ss 5y agoJust watched your video on Voronoi diagrams, Delaunay triangulations, and natural neighbor interpolation. Great stuff. Please keep it up