Implement conv in python (#408)

* Implement conv in python

* Fix conv func

* fix range

* remove numpy usage

* Fix discrete convolution

* Revert julia file

* Add padding for fft

* Make requested changes

Author: jasmaa

contents/convolutions/code/python/conv.py

@@ -0,0 +1,60 @@
+import math
+from scipy.fftpack import fft, ifft
+
+def conv(signal1, signal2):
+    """Discrete convolution by definition"""
+
+    n = len(signal1) + len(signal2) - 1
+    out = []
+    
+    for i in range(n):
+        s = 0
+        
+        for j in range(i + 1):
+            if j < len(signal1) and i - j  < len(signal2):
+                s += signal1[j] * signal2[i - j]
+                
+        out.append(s)
+
+    return out
+
+
+def conv_fft(signal1, signal2):
+    """Convolution using fft and convolutional theorem"""
+
+    signal1 = signal1.copy()
+    signal2 = signal2.copy()
+
+    # pad signals to same len
+    max_len = max(len(signal1), len(signal2))
+    
+    for i in range(max_len - len(signal1)):
+        signal1.append(0)
+    for i in range(max_len - len(signal2)):
+        signal2.append(0)
+    
+    fft_s1 = fft(signal1)
+    fft_s2 = fft(signal2)
+    out = []
+
+    for i in range(len(signal1)):
+        out.append(fft_s1[i] * fft_s2[i])
+
+    return list(ifft(out))
+
+
+def main():
+    # Example convolution with sin and cos
+    s1 = [math.sin(x) for x in range(5)]
+    s2 = [math.cos(x) for x in range(5)]
+
+    print("Discrete Convolution")
+    print(conv(s1, s2))
+
+    print("FFT Convolution")
+    print(conv_fft(s1, s2))
+
+
+if __name__ == "__main__":
+    main()
+

contents/convolutions/convolutions.md

@@ -44,6 +44,8 @@ In code, this looks something like:
 [import:5-18, lang:"c_cpp"](code/c/convolutions.c)
 {% sample lang="cpp"%}
 [import:68-88, lang:"c_cpp"](code/c++/convolutions.cpp)
+{% sample lang="python"%}
+[import:4-19, lang:"python"](code/python/conv.py)
 {% endmethod %}
 
 Note that in this case, the output array will be the size of `f[n]` and `g[n]` put together.
@@ -93,6 +95,8 @@ Where the `.*` operator is an element-wise multiplication.
 [import:20-30, lang:"c_cpp"](code/c/convolutions.c)
 {% sample lang="cpp"%}
 [import:90-105, lang:"c_cpp"](code/c++/convolutions.cpp)
+{% sample lang="python"%}
+[import:22-43, lang:"python"](code/python/conv.py)
 {% endmethod %}
 
 This method also has the added advantage that it will *always output an array of the size of your signal*; however, if your signals are not of equal size, we need to pad the smaller signal with zeros.