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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: |

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