Add circular convolution

electronics/circular_convolution.py

@@ -0,0 +1,99 @@
+# https://en.wikipedia.org/wiki/Circular_convolution
+
+"""
+Circular convolution, also known as cyclic convolution,
+is a special case of periodic convolution, which is the convolution of two
+periodic functions that have the same period. Periodic convolution arises,
+for example, in the context of the discrete-time Fourier transform (DTFT).
+In particular, the DTFT of the product of two discrete sequences is the periodic
+convolution of the DTFTs of the individual sequences. And each DTFT is a periodic
+summation of a continuous Fourier transform function.
+
+Source: https://en.wikipedia.org/wiki/Circular_convolution
+"""
+
+import doctest
+from collections import deque
+
+import numpy as np
+
+
+class CircularConvolution:
+ """
+ This class stores the first and second signal and performs the circular convolution
+ """
+
+ def __init__(self) -> None:
+ """
+ First signal and second signal are stored as 1-D array
+ """
+
+ self.first_signal = [2, 1, 2, -1]
+ self.second_signal = [1, 2, 3, 4]
+
+ def circular_convolution(self) -> list[float]:
+ """
+ This function performs the circular convolution of the first and second signal
+ using matrix method
+
+ Usage:
+ >>> import circular_convolution as cc
+ >>> convolution = cc.CircularConvolution()
+ >>> convolution.circular_convolution()
+ [10, 10, 6, 14]
+
+ >>> convolution.first_signal = [0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6]
+ >>> convolution.second_signal = [0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5]
+ >>> convolution.circular_convolution()
+ [5.2, 6.0, 6.48, 6.64, 6.48, 6.0, 5.2, 4.08]
+
+ >>> convolution.first_signal = [-1, 1, 2, -2]
+ >>> convolution.second_signal = [0.5, 1, -1, 2, 0.75]
+ >>> convolution.circular_convolution()
+ [6.25, -3.0, 1.5, -2.0, -2.75]
+
+ >>> convolution.first_signal = [1, -1, 2, 3, -1]
+ >>> convolution.second_signal = [1, 2, 3]
+ >>> convolution.circular_convolution()
+ [8, -2, 3, 4, 11]
+
+ """
+
+ length_first_signal = len(self.first_signal)
+ length_second_signal = len(self.second_signal)
+
+ max_length = max(length_first_signal, length_second_signal)
+
+ # create a zero matrix of max_length x max_length
+ matrix = [[0] * max_length for i in range(max_length)]
+
+ # fills the smaller signal with zeros to make both signals of same length
+ if length_first_signal < length_second_signal:
+ self.first_signal += [0] * (max_length - length_first_signal)
+ elif length_first_signal > length_second_signal:
+ self.second_signal += [0] * (max_length - length_second_signal)
+
+ """
+ Fills the matrix in the following way assuming 'x' is the signal of length 4
+ [
+ [x[0], x[3], x[2], x[1]],
+ [x[1], x[0], x[3], x[2]],
+ [x[2], x[1], x[0], x[3]],
+ [x[3], x[2], x[1], x[0]]
+ ]
+ """
+ for i in range(max_length):
+ rotated_signal = deque(self.second_signal)
+ rotated_signal.rotate(i)
+ for j, item in enumerate(rotated_signal):
+ matrix[i][j] += item
+
+ # multiply the matrix with the first signal
+ final_signal = np.matmul(np.transpose(matrix), np.transpose(self.first_signal))
+
+ # rounding-off to two decimal places
+ return [round(i, 2) for i in final_signal]
+
+
+if __name__ == "__main__":
+ doctest.testmod()