Circular Convolution using python

Platform → Python 3.8.3 , numpy

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 . — Wikipedia

The algorithm we will be using here ->

# 1 ) input x(n) and h(n)
# 2 ) For circular convolution we need N*N matrix so initializing empty matrix with np.zeros((shape))
# 3 )Copying the x(n) into the first row of the matrix
# 4 ) Run a for loop from 1 st row to Nth row.
# 5 )In each iteration circularly shift the row vector
# 6 )Take transpose of the matrix to get regular form as in circular convolution matrix
# 7 ) Make sure that x(n) and h(n) are of same length .
# 8 ) Multiply generated matrix with matrix h(n)

The code

import numpy as np
# circular shift operation
# [1 2 3 4] = [4 1 2 3]
def shifter(matrix):
    last = matrix[len(matrix)-1]
    x = len(matrix)
    result = [0] * x
    for i in range(1,len(matrix)):
    result[i] = matrix[i-1]
    result[0] = last
    return result
#  finding circular convolution
def findCircularConvolution(x,h,n,m):
    primary_matrix = np.zeros((max(n,m),max(n,m)))
    for i in range(0,len(primary_matrix[0])):
    primary_matrix[0][i] = x[i]
    for i in range(1,max(n,m)):
        primary_matrix[i] = shifter(primary_matrix[i-1])
        ultimate_matrix = np.transpose(primary_matrix)
    difference_in_length = abs(n-m)
    for i in range(m,m+difference_in_length):
         h.append(0)
   resultant = np.dot(ultimate_matrix,h)
   return resultant
x = [int(x) for x in input('Enter the x(n) -> ').split()]
h = [int(x) for x in input('Enter the h(n) -> ').split()]
circular_convolution_result = findCircularConvolution(x,h,len(x),len(h))
print(circular_convolution_result)

Output