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Yeah, this is pretty annoying. Starting with a function from the circle to the complex plane, the Fourier series decomposes it into a sum of exponentials, which
by falseprofit 6y ago
Yeah, this is pretty annoying. Starting with a function from the circle to the complex plane, the Fourier series decomposes it into a sum of exponentials, which are circular motions about 0.
This version with x and y coordinates separated overcomplicates and confuses. And with a four-dimensional output, there are 2 unused dimensions whose values are arbitrary.
- physicles 6y agoI wonder if this means the problem is under-determined (too many degrees of freedom) and that leads to numerical instability. Certainly one set of equations is enough, as 3Blue1Brown’s Fourier transform video shows.