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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]
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 $$ S[f] = \sum_{n=1}^{N}{s[n] \times e^{\frac{fnj2\pi}{N}}} $$ $$ S[f] = \sum_{n=1}^{N}{s[n] \times e^{\frac{fnj2\pi}{N}}} $$
  
-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:​
  
 $$ S[-f] = \sum_{n=1}^{N}{s[n] \times e^{\frac{-fnj2\pi}{N}}} $$ $$ S[-f] = \sum_{n=1}^{N}{s[n] \times e^{\frac{-fnj2\pi}{N}}} $$