Return the discrete linear convolution of two one-dimensional sequences and return the middle values in Python

To return the discrete linear convolution of two one-dimensional sequences, use the numpy.convolve() method in Python Numpy. The convolution operator is often seen in signal processing, where it models the effect of a linear time-invariant system on a signal. In probability theory, the sum of two independent random variables is distributed according to the convolution of their individual distributions. If v is longer than a, the arrays are swapped before computation.

The method returns the Discrete, linear convolution of a and v. The 1st parameter, a is the first onedimensional input array. The 2nd parameter, v is the second one-dimensional input array. The 3rd parameter, mode is optional, with values full’, ‘valid’, ‘same’. The mode ‘same’ returns output of length max(M, N). Boundary effects are still visible.

Steps

At first, import the required libraries −

import numpy as np

Creating two numpy One-Dimensional array using the array() method −

arr1 = np.array([1, 2, 3])
arr2 = np.array([0, 1, 0.5])

Display the arrays −

print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

Check the Dimensions of both the arrays −

print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

Check the Shape of both the arrays −

print("\nShape of Array1...\n",arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

To return the discrete linear convolution of two one-dimensional sequences, use the numpy.convolve() method −

print("\nResult....\n",np.convolve(arr1, arr2, mode = 'same' ))

Example

import numpy as np

# Creating two numpy One-Dimensional array using the array() method
arr1 = np.array([1, 2, 3])
arr2 = np.array([0, 1, 0.5])

# Display the arrays
print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

# Check the Shape of both the arrays
print("\nShape of Array1...\n",arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

# To return the discrete linear convolution of two one-dimensional sequences, use the numpy.convolve() method in Python Numpy
print("\nResult....\n",np.convolve(arr1, arr2, mode = 'same' ))

Output

Array1...
[1 2 3]

Array2...
[0. 1. 0.5]

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(3,)

Shape of Array2...
(3,)

Result....
[1. 2.5 4. ]