Convolution with np.convolve() in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of simple 1D convolution

What is the output of this code using np.convolve() with default mode?

NumPy

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

A [0. 1. 2.5 4. 1.5]

B [1. 2. 3. 0. 0.5]

C [0. 1. 2. 3. 1.5]

D [0. 1. 2.5 3. 1.5]

💡 Hint

Remember that default mode is 'full' which gives the complete convolution result.

The convolution sums overlapping products of x and h. The output length is len(x)+len(h)-1 = 5. Calculating stepwise: 0*1=0, 1*1=1, (2*1 + 1*0.5)=2.5, (3*1 + 2*0.5)=4, 3*0.5=1.5.

❓ data_output

intermediate

Length of convolution output with 'valid' mode

Given two arrays a = np.array([1, 2, 3, 4]) and b = np.array([1, 0, -1]), what is the length of the output when convolving with mode='valid'?

NumPy

import numpy as np
a = np.array([1, 2, 3, 4])
b = np.array([1, 0, -1])
result = np.convolve(a, b, mode='valid')
print(len(result))

A 4

B 2

C 3

D 6

💡 Hint

Length in 'valid' mode is max(len(a), len(b)) - min(len(a), len(b)) + 1.

For 'valid' mode, output length is len(a) - len(b) + 1 = 4 - 3 + 1 = 2, so answer is 2.

🔧 Debug

advanced

Identify the error in convolution code

What error does this code raise when run?

NumPy

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

A TypeError: object of type 'numpy.ndarray' has no len()

B ValueError: object too deep for desired array

C TypeError: cannot perform reduce with flexible type

D TypeError: 1D arrays expected

💡 Hint

Check the shape of the arrays passed to np.convolve.

np.convolve expects 1D arrays. Here, h is 2D (shape (1,3)) which causes a TypeError indicating 1D arrays expected.

🧠 Conceptual

advanced

Effect of 'same' mode in np.convolve()

Which statement best describes the output length when using np.convolve(a, b, mode='same')?

A Output length matches the length of the first input array.

B Output length is the maximum of the two input lengths.

C Output length matches the length of the second input array.

D Output length is always the sum of input lengths minus one.

💡 Hint

The 'same' mode centers the full convolution output to match the first input's length.

In 'same' mode, np.convolve returns an output array with the same length as the first input array, centered with respect to the full convolution.

🚀 Application

expert

Using convolution to compute moving average

You want to compute a simple moving average of window size 3 on array data = np.array([1, 2, 3, 4, 5]). Which np.convolve() call produces the correct moving average values aligned with the original data length?

A np.convolve(data, np.ones(3)/3, mode='full')

B np.convolve(data, np.ones(3)/3, mode='valid')

C np.convolve(data, np.ones(3)/3, mode='same')

D np.convolve(data, np.ones(3), mode='same') / 3

💡 Hint

Moving average should have the same length as data and average over 3 points centered.

Using mode='same' with kernel np.ones(3)/3 gives a moving average aligned with the original data length. 'valid' mode shortens output, 'full' extends it, and option C divides after convolution with unnormalized kernel causing wrong values.