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# Return the discrete linear convolution of two one-dimensional sequences and get where they overlap 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 one-dimensional 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 ‘valid’ returns output of length max(M, N) - min(M, N) + 1. The convolution product is only given for points where the signals overlap completely. Values outside the signal boundary have no effect.

## 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 in Python Numpy −

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

## 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 = 'valid' ))

## 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.... [2.5]