Convolution (convolve) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of 1D convolution with 'full' mode

What is the output of this code snippet using scipy.signal.convolve with mode='full'?

SciPy

import numpy as np
from scipy.signal import convolve

x = np.array([1, 2, 3])
h = np.array([0, 1, 0.5])
result = convolve(x, h, mode='full')
print(result)

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

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

C [0. 1. 2.5 4. 1.5]

D [1. 2.5 4. 1.5 0. ]

💡 Hint

Remember that 'full' mode returns the complete convolution, including edges.

The convolution sums products of overlapping elements. With mode='full', the output length is len(x)+len(h)-1 = 5. The calculation yields [0, 1, 2.5, 4, 1.5].

❓ data_output

intermediate

Length of convolution result with 'valid' mode

Given two arrays a and b of lengths 7 and 3 respectively, what is the length of the result when convolving with mode='valid'?

SciPy

from scipy.signal import convolve

a = [1,2,3,4,5,6,7]
b = [0,1,0.5]
result = convolve(a, b, mode='valid')
print(len(result))

A 7

B 5

C 9

D 3

💡 Hint

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

In 'valid' mode, convolution only includes points where arrays fully overlap, so length is 7 - 3 + 1 = 5.

🔧 Debug

advanced

Identify the error in convolution code

What error will this code raise when run?

SciPy

import numpy as np
from scipy.signal import convolve

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

A ValueError: x and h must have the same number of dimensions

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

C No error, prints a 2D convolution result

D IndexError: index out of bounds

💡 Hint

Check the shapes of the input arrays for convolution.

The 1D array x and 2D array h have different dimensions, so convolve raises a ValueError about dimension mismatch.

❓ visualization

advanced

Plotting convolution result of two signals

Which option correctly plots the convolution of two signals x and h using matplotlib?

SciPy

import numpy as np
from scipy.signal import convolve
import matplotlib.pyplot as plt

x = np.array([1, 2, 3, 4])
h = np.array([0, 1, 0.5])
result = convolve(x, h, mode='full')

# Plot code here

A plt.plot(result); plt.title('Convolution Result'); plt.show()

B plt.scatter(range(len(result)), result); plt.title('Convolution Result'); plt.show()

C plt.bar(range(len(result)), result); plt.title('Convolution Result'); plt.show()

D plt.stem(result); plt.title('Convolution Result'); plt.show()

💡 Hint

Use a line plot to show the convolution values clearly.

Using plt.plot shows the convolution as a continuous line, which is standard for signal visualization. Other plots are less clear or less common for this data.

🧠 Conceptual

expert

Effect of convolution mode on output size

Which statement correctly describes the relationship between input sizes and output size for scipy.signal.convolve modes?

A 'full' mode output length equals len(x); 'valid' mode output length equals len(h); 'same' mode output length equals len(x) - len(h) + 1

B 'full' mode output length equals max(len(x), len(h)); 'valid' mode output length equals min(len(x), len(h)); 'same' mode output length is len(x) + len(h) - 1

C 'full' mode output length is len(x) - len(h) + 1; 'valid' mode output length is len(x) + len(h) - 1; 'same' mode output length equals len(h)

D 'full' mode output length is len(x) + len(h) - 1; 'valid' mode output length is len(x) - len(h) + 1; 'same' mode output length equals len(x)

💡 Hint

Recall the definitions of convolution modes and their output sizes.

'full' mode returns the complete convolution with length len(x)+len(h)-1. 'valid' mode returns only points where arrays fully overlap, length len(x)-len(h)+1. 'same' mode returns output the same size as the first input.