From d705228b483fe35e5e9fed7f236b353d135bfdcc Mon Sep 17 00:00:00 2001
From: Loic Guegan <manzerbredes@mailbox.org>
Date: Thu, 2 Nov 2023 06:41:29 +0100
Subject: [PATCH] Minor changes

---
 source/signal_processing/code/dft.R | 20 ++++++++++++++++++++
 source/signal_processing/dft.rst    |  1 +
 2 files changed, 21 insertions(+)
 create mode 100644 source/signal_processing/code/dft.R

diff --git a/source/signal_processing/code/dft.R b/source/signal_processing/code/dft.R
new file mode 100644
index 0000000..3420387
--- /dev/null
+++ b/source/signal_processing/code/dft.R
@@ -0,0 +1,20 @@
+x=c(1,2,3,4) # Our real signal
+N=4 # Signal size
+fs=10 # Sampling frequency
+Xkn=function(k,n){x[n+1]*exp(-2i*pi*(k/N)*n)}
+
+# Compute DFT:
+X0=Xkn(0,0)+Xkn(0,1)+Xkn(0,2)+Xkn(0,3)
+X1=Xkn(1,0)+Xkn(1,1)+Xkn(1,2)+Xkn(1,3)
+X2=Xkn(2,0)+Xkn(2,1)+Xkn(2,2)+Xkn(2,3)
+X3=Xkn(3,0)+Xkn(3,1)+Xkn(3,2)+Xkn(3,3)
+
+X=c(X0,X1,X2,X3) # This is your final fft
+
+f0=0/N*fs # k/N*fs
+f1=1/N*fs
+f2=2/N*fs
+f3=3/N*fs
+
+# Plot FFT:
+plot(c(-f3,-f2,-f1,f0,f1,f2,f3),c(X3,X2,X1,X0,X1,X2,X3),type="l", xlab="Frequency (Hz)", ylab="Amplitude (Volt, db etc..)")
diff --git a/source/signal_processing/dft.rst b/source/signal_processing/dft.rst
index 59df92c..72ec952 100644
--- a/source/signal_processing/dft.rst
+++ b/source/signal_processing/dft.rst
@@ -44,3 +44,4 @@ In depth example
 
 Let's take a discrete signal :math:`\vec{x}=\{1,2,3,4\}`, sampled at a frequency :math:`f_s=10 Hz`.
 
+.. literalinclude:: code/dft.R