Correlation with np.correlate() in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.correlate with mode='valid'

What is the output of the following code snippet?

NumPy

import numpy as np
x = np.array([1, 2, 3])
y = np.array([0, 1, 0.5])
result = np.correlate(x, y, mode='valid')
print(result)

A [2.0 3.5 3.0]

B [3.5]

C [2.5]

D [0.5 2.0 3.5]

💡 Hint

Remember that mode='valid' returns only positions where the signals fully overlap.

np.correlate with mode='valid' computes the sum of products where the two arrays fully overlap. Here, it computes 1*0.5 + 2*1 + 3*0 = 0.5 + 2 + 0 = 2.5, because np.correlate reverses the second array before computing the sum of products.

❓ data_output

intermediate

Length of output array from np.correlate with mode='full'

Given two arrays of lengths 4 and 3, what is the length of the output array when using np.correlate with mode='full'?

NumPy

import numpy as np
x = np.array([1, 2, 3, 4])
y = np.array([0, 1, 0.5])
result = np.correlate(x, y, mode='full')
print(len(result))

A 3

B 6

C 7

D 4

💡 Hint

The length of the full correlation output is length(x) + length(y) - 1.

For mode='full', the output length is the sum of input lengths minus 1. Here, 4 + 3 - 1 = 6. The correct length is 6, so option B is correct. Option B says 7, which is incorrect.

🔧 Debug

advanced

Identify the error in np.correlate usage

What error does the following code raise?

NumPy

import numpy as np
x = np.array([1, 2, 3])
y = np.array([[0, 1, 0.5]])
result = np.correlate(x, y)
print(result)

A TypeError: np.correlate() only supports 1D arrays

B ValueError: object too deep for desired array

C No error, prints the correlation result

D TypeError: unsupported operand type(s) for *: 'int' and 'list'

💡 Hint

Check the shape of the input arrays; np.correlate expects 1D arrays.

np.correlate only works with 1D arrays. Here, y is a 2D array with shape (1,3), which causes a TypeError indicating np.correlate only supports 1D arrays.

🧠 Conceptual

advanced

Effect of reversing the second array in np.correlate

Which statement best describes how np.correlate computes correlation between two arrays x and y?

A np.correlate computes the sum of element-wise products of x and the reversed y.

B np.correlate computes the convolution of x and y without reversing any array.

C np.correlate computes the sum of element-wise products of x and y without reversing y.

D np.correlate computes the sum of element-wise products of reversed x and y.

💡 Hint

Correlation involves flipping one of the signals before sliding.

np.correlate computes the sum of products between x and the reversed y array, sliding y over x. This is the definition of cross-correlation.

🚀 Application

expert

Find the lag with maximum correlation

Given two 1D numpy arrays x and y, which code snippet correctly finds the lag (shift) where their correlation is maximum using np.correlate with mode='full'?

NumPy

import numpy as np
x = np.array([1, 3, 2, 4])
y = np.array([0, 1, 0.5, 1])

A

corr = np.correlate(x[::-1], y, mode='full')
lag = np.argmax(corr) - (len(y) - 1)
print(lag)

B

corr = np.correlate(x, y, mode='valid')
lag = np.argmax(corr)
print(lag)

C

corr = np.correlate(x, y[::-1], mode='full')
lag = np.argmax(corr) - (len(x) - 1)
print(lag)

D

corr = np.correlate(x, y, mode='full')
lag = np.argmax(corr) - (len(y) - 1)
print(lag)

💡 Hint

The lag index is offset by the length of the second array minus one in full mode.

Using mode='full', the correlation array length is len(x)+len(y)-1. The zero lag corresponds to index len(y)-1. So subtracting (len(y)-1) from the argmax index gives the lag where correlation is maximum.