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8 votes

Taking derivative using FFT

I believe this stems from the fact that your function $f(x) = x^2$ does not have continuous derivatives once it is extended periodically like $$\tilde{f}(x) = f(x \ \mathrm{mod} \ 12 -6),$$ which ...
whpowell96's user avatar
  • 2,478
6 votes

Can this finite difference dispersion be eliminated somehow?

It isn't the spike that's causing the dispersion. The scheme you use has a dispersion relationship whereby waves of different frequency travel at different speeds. Every numerical scheme has such a ...
Wolfgang Bangerth's user avatar
2 votes

Error propagation through an FFT

In Higham's book there is throughout and easily understandable treatment of the error in the Cooley-Tuckey algorithm. Unluckily the matrix pproach proposed by mathew gunther leds to overestimates, ...
Orkolorj9's user avatar
2 votes

Fourier Transform with logarithmic spacing?

This problem can be addressed by using a Constant Q transform instead of the ordinary Fourier transform. This functionally is provided, for example, by the python library Librosa. The constant Q ...
KF Gauss's user avatar
  • 171
1 vote

Prediction of sphere (i.e. roast) core temperature heated in an oven

Below is my wild guess at estimating the core temperature using a simplified version of the temperature at the center of a sphere. It "looks good", but the good look comes at the price of a ...
Dieter Menne's user avatar
1 vote

Error propagation through an FFT

This has been derived in G. Betta, C. Liguori, and A. Pietrosanto "Propagation of uncertainty in a discrete Fourier transform algorithm, " Measurement, vol. 27, no. 4, pp. 231-239, Jun. 2000....
student1's user avatar
  • 121

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