diff --git a/electronics/circular_convolution.py b/electronics/circular_convolution.py new file mode 100644 index 000000000..f2e35742e --- /dev/null +++ b/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()