Add circular convolution

electronics/circular_convolution.py

@@ -0,0 +1,101 @@
+# 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 for i in range(max_length - length_first_signal)]
+        elif length_first_signal > length_second_signal:
+            self.second_signal += [0 for i in range(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 in range(max_length):
+                matrix[i][j] += rotated_signal[j]
+
+        # 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
+        final_signal = [round(i, 2) for i in final_signal]
+
+        return final_signal
+
+
+if __name__ == "__main__":
+    doctest.testmod()