Why windowing is needed in Signal Processing - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to apply a window function to a signal array.

Signal Processing

import numpy as np
signal = np.array([1, 2, 3, 4, 5])
window = np.[1](len(signal))
windowed_signal = signal * window

Drag options to blanks, or click blank then click option'

Ahanning

Brandom

Czeros

Dones

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'ones' window does not reduce edge effects.

Using 'zeros' window will zero out the signal.

Using 'random' window adds noise.

The hanning function creates a window that tapers the signal edges smoothly, reducing spectral leakage.

2fill in blank

medium

Complete the code to compute the Fourier Transform of a windowed signal.

Signal Processing

import numpy as np
signal = np.array([1, 2, 3, 4, 5])
window = np.hanning(len(signal))
windowed_signal = signal * window
spectrum = np.fft.[1](windowed_signal)

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Aifft

Brfft

Cfft

Dfftshift

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'ifft' computes inverse transform, not spectrum.

Using 'fftshift' rearranges spectrum but does not compute it.

Using 'rfft' is for real inputs but less general.

The fft function computes the Fourier Transform, showing frequency components of the windowed signal.

3fill in blank

hard

Fix the error in the code to avoid spectral leakage by applying windowing before FFT.

Signal Processing

import numpy as np
signal = np.array([1, 2, 3, 4, 5])
windowed_signal = signal * [1]
spectrum = np.fft.fft(windowed_signal)

Drag options to blanks, or click blank then click option'

Anp.hanning(len(signal))

Bnp.random.rand(len(signal))

Cnp.zeros(len(signal))

Dnp.ones(len(signal))

Attempts:

3 left

💡 Hint

Common Mistakes

Using ones does not reduce leakage.

Using zeros removes the signal.

Using random adds noise.

Applying the Hanning window before FFT reduces spectral leakage by tapering signal edges.

4fill in blank

hard

Fill both blanks to create a windowed signal and compute its magnitude spectrum.

Signal Processing

import numpy as np
signal = np.array([1, 2, 3, 4, 5])
window = np.[1](len(signal))
windowed_signal = signal * window
magnitude = np.abs(np.fft.[2](windowed_signal))

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Ahamming

Bfft

Cifft

Dblackman

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'ifft' instead of 'fft' for spectrum.

Using 'blackman' window is valid but not the expected answer here.

Mixing window and transform functions.

The hamming window reduces spectral leakage, and fft computes the frequency spectrum. Taking absolute value gives magnitude.

5fill in blank

hard

Fill all three blanks to create a windowed signal, compute its FFT, and normalize the magnitude.

Signal Processing

import numpy as np
signal = np.array([1, 2, 3, 4, 5])
window = np.[1](len(signal))
windowed_signal = signal * window
spectrum = np.fft.[2](windowed_signal)
magnitude = np.abs(spectrum) / [3](window)

Drag options to blanks, or click blank then click option'

Ablackman

Bfft

Csum

Dhanning

Attempts:

3 left

💡 Hint

Common Mistakes

Using blackman window is valid but not the expected here.

Not normalizing magnitude leads to incorrect scale.

Using ifft instead of fft.

The hanning window tapers the signal, fft computes the spectrum, and dividing by sum(window) normalizes the magnitude.