added convolutional theorem implementation in python (#869)

* added convolutional theorem implementation in python

* fixed chapter linking

* added comments to the code

* changed random distribution to sawtooth

* corrected previous commit

* fixed comments

Co-authored-by: James Schloss <jrs.schloss@gmail.com>

Author: pillarxyz

contents/convolutions/convolutional_theorem/code/python/convolutional_theorem.py

@@ -0,0 +1,19 @@
+from scipy.fft import fft, ifft
+import numpy as np
+
+# using the convolutional theorem
+def convolve_fft(signal1, signal2):
+    return ifft(np.multiply(fft(signal1),fft(signal2)))
+
+# Sawtooth functions
+x = [float(i)/200 for i in range(1,101)]
+y = [float(i)/200 for i in range(1,101)]
+
+x /= np.linalg.norm(x)
+y /= np.linalg.norm(y)
+
+# Convolving the two signals
+fft_output = convolve_fft(x, y)
+
+np.savetxt("fft.dat", np.real(fft_output))
+

contents/convolutions/convolutional_theorem/convolutional_theorem.md

@@ -44,6 +44,8 @@ For this example code, we will be using two sawtooth functions as we did in the
 {% method %}
 {% sample lang="jl" %}
 [import, lang:"julia"](code/julia/convolutional_theorem.jl)
+{% sample lang="py" %}
+[import, lang:"python"](code/python/convolutional_theorem.py)
 {% endmethod %}
 
 This should produce the following output:
@@ -52,7 +54,6 @@ This should produce the following output:
     <img class="center" src="../res/cyclic.png" style="width:75%">
 </p>
 
-
 <script>
 MathJax.Hub.Queue(["Typeset",MathJax.Hub]);
 </script>