This analysis is just wrong; the Gibbs phenomenon is not some impossible law that you cannot avoid. The Gibbs phenomenon appears only when you have truncated Fourier series; if you drop off more gradually towards the last term (e.g., a cos²- or sinc-scaled dropoff), the phenomenon disappears. Of course, this would be at the cost of a worse mean-squared error, but for most purposes, this is a good tradeoff. If you moved binary stars around, and they indeed had infinitely sharp frequency spectra, surely you would not go for the solution with the most truncation :-)
2 comments
[ 0.22 ms ] story [ 102 ms ] thread