Rectangular window limitations in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a rectangular window of length 50 using NumPy.

Signal Processing

import numpy as np
window = np.[1](50)

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Ablackman

Bhanning

Cones

Dhamming

Attempts:

3 left

💡 Hint

Common Mistakes

Using other window functions like hamming or hanning instead of ones.

Confusing the window length with the window type.

The rectangular window is created by an array of ones, so np.ones is used.

2fill in blank

medium

Complete the code to compute the Fourier Transform of the rectangular window using NumPy's FFT.

Signal Processing

import numpy as np
window = np.ones(50)
fft_window = np.fft.[1](window)

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Afft

Bfftshift

Crfft

Difft

Attempts:

3 left

💡 Hint

Common Mistakes

Using inverse FFT instead of FFT.

Using FFT shift which only rearranges the FFT output.

The Fourier Transform is computed using np.fft.fft.

3fill in blank

hard

Fix the error in the code to plot the magnitude of the FFT of the rectangular window using matplotlib.

Signal Processing

import numpy as np
import matplotlib.pyplot as plt
window = np.ones(50)
fft_window = np.fft.fft(window)
plt.plot(np.abs(fft_window[1]))
plt.title('Magnitude of FFT of Rectangular Window')
plt.show()

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A[:25]

B[0:25]

C[0:50]

D[:50]

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect slice notation like [0:25] which is valid but less common.

Trying to slice with [0:50] which is the full length and unnecessary.

To plot the first half of the FFT magnitude, slice with [:25].

4fill in blank

hard

Fill in the blank to create a dictionary of window lengths and their main lobe widths, assuming main lobe width is 2 divided by window length.

Signal Processing

window_lengths = [20, 40, 80]
main_lobe_widths = {length: 2 [1] length for length in window_lengths}

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A+

B/

C*

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of division for main lobe width.

Not iterating over the list correctly.

The main lobe width is calculated as 2 divided by each window length, so the expression is 2 / length. The dictionary comprehension iterates over window_lengths.

5fill in blank

hard

Fill all three blanks to create a plot comparing the rectangular window and its FFT magnitude normalized by the maximum value.

Signal Processing

import numpy as np
import matplotlib.pyplot as plt
N = 50
window = np.ones(N)
fft_window = np.fft.fft(window)
fft_magnitude = np.abs(fft_window) / np.[1](np.abs(fft_window))
plt.plot(window, label='Rectangular Window')
plt.plot(fft_magnitude[:N//2], label='Normalized FFT Magnitude')
plt.[2]('Window Samples')
plt.[3]('Amplitude')
plt.legend()
plt.show()

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Amin

Bxlabel

Cylabel

Dmax

Attempts:

3 left

💡 Hint

Common Mistakes

Using min instead of max for normalization.

Mixing up xlabel and ylabel functions.

The FFT magnitude is normalized by its maximum value using np.max. The x-axis label is set with plt.xlabel and the y-axis label with plt.ylabel.