Minor changes

source/index.rst

@@ -26,6 +26,7 @@ Welcome to ScienceNotes's documentation!
    :caption: Signal Processing
 
    signal_processing/fourier_tables.rst
+   signal_processing/dft.rst
 
 Indices and tables
 ==================

source/signal_processing/dft.rst

@@ -0,0 +1,25 @@
+Discrete Fourier Transform
+----------------------------
+
+Discrete Fourier Transform (DFT) is used to perform the Fourier transform of a discrete signal.
+The DFT of a discrete complex/real signal :math:`\vec{x}={x_0,...,x_{N-1}}` is:
+
+.. math::
+   X_k = \sum_{n=0}^{N-1} x_n \cdot e^{-j2\pi\frac{k}{N}n}
+
+.. note::
+   In this case, :math:`\frac{k}{N}` can be seen as the frequency of the wave used to determined
+   the :math:`k^{th}` frequency :math:`X_k`.
+   See `here <https://www.youtube.com/watch?v=mkGsMWi_j4Q&t=282s>`__ for more infos.
+
+The inverse DFT of a discrete complex/real signal :math:`\vec{x}={x_0,...,x_{N-1}}` is:
+
+.. math::
+   x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k \cdot e^{j2\pi\frac{k}{N}n}
+
+.. note::
+   If the signal is *real*, all the complex terms of the inverse DFT are suppose to cancel out.
+
+In depth example
+=================
+