Spectral leakage concept in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a simple sine wave signal.

Signal Processing

import numpy as np
fs = 1000  # Sampling frequency
f = 5     # Frequency of the sine wave
t = np.arange(0, 1, 1/fs)
signal = np.sin(2 * np.pi * [1] * t)

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Afs

Bf

Ct

Dnp.pi

Attempts:

3 left

💡 Hint

Common Mistakes

Using sampling frequency fs instead of signal frequency f.

The sine wave frequency is given by f, so it should multiply 2 * np.pi * f * t.

2fill in blank

medium

Complete the code to compute the FFT of the signal.

Signal Processing

from numpy.fft import fft
N = len(signal)
fft_values = fft([1])

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At

BN

Csignal

Dfs

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the time vector t instead of the signal.

The FFT should be computed on the signal data, which is stored in signal.

3fill in blank

hard

Fix the error in the code to correctly compute the frequency bins for the FFT.

Signal Processing

freqs = np.fft.fftfreq([1], d=1/fs)

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AN

Bfs

Csignal

Dt

Attempts:

3 left

💡 Hint

Common Mistakes

Passing sampling frequency fs instead of number of samples N.

The fftfreq function needs the number of samples N and the sample spacing d=1/fs.

4fill in blank

hard

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

Signal Processing

window = np.[1](N)
windowed_signal = signal * window
fft_windowed = np.fft.[2](windowed_signal)

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Ahanning

Bhamming

Cfft

Difft

Attempts:

3 left

💡 Hint

Common Mistakes

Using ifft instead of fft.

Using hanning when the question expects hamming.

Applying a Hamming window reduces spectral leakage. Then compute FFT with fft.

5fill in blank

hard

Fill both blanks to create a dictionary of frequency magnitudes above a threshold.

Signal Processing

threshold = 10
freq_magnitudes = {freq: abs(fft_windowed[i]) [1] threshold for i, freq in enumerate(freqs) if freq >= 0 and abs(fft_windowed[i]) [2] threshold}

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A:

B>

C>=

D,

Attempts:

3 left

💡 Hint

Common Mistakes

Using comma , instead of colon : in dictionary comprehension.

Using >= instead of > inconsistently.

The dictionary comprehension syntax requires a colon : between key and value. We filter frequencies and magnitudes greater than the threshold using >.