Real FFT (rfft) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute the real FFT of the signal array.

SciPy

import numpy as np
from scipy.fft import [1]
signal = np.array([0, 1, 0, -1])
result = [1](signal)

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Arfft

Bfft

Cifft

Dirfft

Attempts:

3 left

💡 Hint

Common Mistakes

Using fft instead of rfft causes output to be complex and longer.

Using ifft or irfft is for inverse transforms, not forward.

The function rfft computes the real FFT of a real-valued input signal.

2fill in blank

medium

Complete the code to compute the frequencies corresponding to the rfft output.

SciPy

import numpy as np
from scipy.fft import rfft, [1]
signal = np.array([0, 1, 0, -1])
sample_rate = 4
freqs = [1](len(signal), 1/sample_rate)

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Afftfreq

Bfftshift

Cirfft

Drfftfreq

Attempts:

3 left

💡 Hint

Common Mistakes

Using fftfreq returns frequencies for full FFT, not real FFT.

Using irfft or fftshift does not return frequencies.

rfftfreq returns the sample frequencies for the output of rfft.

3fill in blank

hard

Fix the error in the code to correctly compute the inverse real FFT.

SciPy

import numpy as np
from scipy.fft import rfft, [1]
signal = np.array([0, 1, 0, -1])
transformed = rfft(signal)
recovered = [1](transformed)

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Aifft

Birfft

Crfft

Dfft

Attempts:

3 left

💡 Hint

Common Mistakes

Using ifft instead of irfft may cause shape mismatch.

Using rfft or fft again does not invert the transform.

irfft computes the inverse of rfft, recovering the original real signal.

4fill in blank

hard

Fill both blanks to create a dictionary of frequencies and their corresponding rfft magnitudes.

SciPy

import numpy as np
from scipy.fft import rfft, rfftfreq
signal = np.array([0, 1, 0, -1])
sample_rate = 4
freqs = [1](len(signal), 1/sample_rate)
magnitudes = np.abs([2](signal))
result = dict(zip(freqs, magnitudes))

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Arfftfreq

Brfft

Cfft

Dirfft

Attempts:

3 left

💡 Hint

Common Mistakes

Using fft instead of rfft causes mismatch in frequencies and magnitudes.

Using irfft instead of rfft for magnitudes is incorrect.

rfftfreq gives frequencies for rfft output; rfft computes the transform.

5fill in blank

hard

Fill all three blanks to compute the normalized power spectrum of a real signal.

SciPy

import numpy as np
from scipy.fft import rfft, rfftfreq
signal = np.array([0, 1, 0, -1])
sample_rate = 4
freqs = [1](len(signal), 1/sample_rate)
transform = [2](signal)
power = np.square(np.abs(transform)) / [3](signal)

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Arfftfreq

Brfft

Cfloat

Dlen

Attempts:

3 left

💡 Hint

Common Mistakes

Using float(len(signal)) instead of len(signal) causes type issues.

Using fftfreq instead of rfftfreq causes frequency mismatch.

rfftfreq gets frequencies; rfft computes transform; len(signal) normalizes power.