2D FFT (fft2) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of 2D FFT on a simple matrix

What is the output of the following code using scipy.fft.fft2 on a 2x2 matrix?

SciPy

import numpy as np
from scipy.fft import fft2

matrix = np.array([[1, 2], [3, 4]])
result = fft2(matrix)
print(np.round(result, 2))

A

[[10.+0.j  2.+0.j]
 [ 4.+0.j  0.+0.j]]

B

[[10.+0.j  2.+0.j]
 [-4.+0.j  0.+0.j]]

C

[[10.+0.j -2.+0.j]
 [ 4.+0.j  0.+0.j]]

D

[[10.+0.j -2.+0.j]
 [-4.+0.j  0.+0.j]]

💡 Hint

Recall that 2D FFT sums over rows and columns with complex exponentials.

The 2D FFT of the matrix [[1,2],[3,4]] results in [[10, -2], [-4, 0]] with zero imaginary parts. This matches option D.

❓ data_output

intermediate

Shape of 2D FFT result

If you apply scipy.fft.fft2 to a 5x3 matrix, what will be the shape of the output?

SciPy

import numpy as np
from scipy.fft import fft2

matrix = np.random.rand(5,3)
result = fft2(matrix)
print(result.shape)

A (8, 8)

B (3, 5)

C (5, 3)

D (1, 1)

💡 Hint

The FFT output shape matches the input shape unless specified otherwise.

The 2D FFT output shape is the same as the input matrix shape by default.

❓ visualization

advanced

Visualizing magnitude spectrum of 2D FFT

Which option correctly plots the magnitude spectrum of the 2D FFT of a 256x256 image stored in image?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.fft import fft2, fftshift

# image is a 256x256 numpy array
f_transform = fft2(image)
f_shifted = fftshift(f_transform)
magnitude_spectrum = np.abs(f_shifted)
plt.imshow(np.log1p(magnitude_spectrum), cmap='gray')
plt.title('Magnitude Spectrum')
plt.show()

A Use fft2, plot magnitude spectrum directly without fftshift or log scale.

B Use fft2, then fftshift, then plot log of magnitude spectrum with gray colormap.

C Use fftshift first, then fft2, then plot magnitude spectrum with jet colormap.

D Plot the real part of fft2 output without any transformation or scaling.

💡 Hint

Centering the zero frequency with fftshift and using log scale helps visualize details.

Option B correctly applies fft2, shifts zero frequency to center, takes magnitude, applies log scale, and plots in grayscale for clear visualization.

🧠 Conceptual

advanced

Effect of zero-padding on 2D FFT resolution

What is the main effect of zero-padding a 2D signal before applying fft2?

A It increases frequency resolution by interpolating the FFT output.

B It changes the original frequency content of the signal.

C It removes noise from the signal before FFT.

D It reduces the computation time of the FFT.

💡 Hint

Think about how zero-padding affects the FFT output size and frequency bins.

Zero-padding adds more points, increasing the number of frequency bins, which interpolates the FFT and improves frequency resolution without changing original frequencies.

🔧 Debug

expert

Identify the error in 2D FFT magnitude calculation

What error will this code raise when calculating the magnitude of a 2D FFT result?

SciPy

import numpy as np
from scipy.fft import fft2

matrix = np.array([[1, 2], [3, 4]])
result = fft2(matrix)
magnitude = np.abs(result.real)
print(magnitude)

A No error, but magnitude is incorrect because it uses only real part.

B TypeError because np.abs cannot be applied to real numbers.

C ValueError due to shape mismatch in np.abs call.

D SyntaxError due to missing parentheses.

💡 Hint

Check how magnitude should be calculated from complex numbers.

The code runs without error but magnitude is wrong because it takes absolute value of only the real part, ignoring imaginary parts.