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Loic Guegan 2023-11-02 07:19:24 +01:00
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source/signal_processing/dft.rst
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@ -27,6 +27,10 @@ Hence, all :math:`X_k` such that :math:`k > \frac{N}{2}` corresponds to negative
&=X_{-1} &=X_{-1}
This explanation is extracted from `here <https://dsp.stackexchange.com/questions/50505/why-is-the-second-half-of-the-fft-negative-frequencies>`__. This explanation is extracted from `here <https://dsp.stackexchange.com/questions/50505/why-is-the-second-half-of-the-fft-negative-frequencies>`__.
Note that, the frequency corresponding to :math:`\frac{N}{2}` is called `Nyquist_rate <https://en.wikipedia.org/wiki/Nyquist_rate>`__.
As frequencies above :math:`\frac{N}{2}` cannot be captured by the signal due to the `Nyquist-Shannon <https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem>`__, a reasoning phenomenon starts to arise.
This leads to a capturing effect of the negative frequencies.
See `here <https://www.youtube.com/watch?v=nOLuVNhBIg0>`__ for a visual explanation.
Inverse DFT Inverse DFT
=========== ===========