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 tutorials:fouriertransformcomputation [2020/07/16 21:42]justin [Three weird little tricks for computing the Fourier Transform] tutorials:fouriertransformcomputation [2020/07/16 21:43] (current)justin [Three weird little tricks for computing the Fourier Transform] Both sides previous revision Previous revision 2020/07/16 21:43 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 21:42 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 21:37 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 21:20 justin [Calculating amplitude (correlation view)] 2020/07/16 20:51 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 20:47 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 20:43 justin [Computation of Fourier transform] 2020/07/16 20:42 justin [Computation of Fourier transform] 2020/07/16 20:40 justin created 2020/07/16 21:43 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 21:42 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 21:37 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 21:20 justin [Calculating amplitude (correlation view)] 2020/07/16 20:51 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 20:47 justin [Three weird little tricks for computing the Fourier Transform] 2020/07/16 20:43 justin [Computation of Fourier transform] 2020/07/16 20:42 justin [Computation of Fourier transform] 2020/07/16 20:40 justin created Line 257: Line 257: $$S[f] = \sum_{n=1}^{N}{s[n] \times e^{\frac{fnj2\pi}{N}}}$$ $$S[f] = \sum_{n=1}^{N}{s[n] \times e^{\frac{fnj2\pi}{N}}}$$ - This means, that for each frequency f, from 1 to N/2, we compute the above projection. Note that the complex exponential is being evaluated at 1/N, 2/N,.. 1. This projection gives us the Fourier coefficient as a complex number and plop it into the vector S. We also need the negative frequencies:​ + This means, that for each frequency f, from 1 to N/2, we compute the above projection. Note that the complex exponential is being evaluated at 1/N, 2/N,.. 1, and we have added in the f so that it is computed for different frequencies. This projection gives us the Fourier coefficient as a complex number and plop it into the vector S. We also need the negative frequencies:​ $$S[-f] = \sum_{n=1}^{N}{s[n] \times e^{\frac{-fnj2\pi}{N}}}$$ $$S[-f] = \sum_{n=1}^{N}{s[n] \times e^{\frac{-fnj2\pi}{N}}}$$