FFT with np.fft module in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the FFT function from numpy's fft module.

NumPy

from numpy.fft import [1]

signal = [1, 2, 3, 4]
fft_result = [1](signal)

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

Aifft

Bfftshift

Cfft

Drfft

Attempts:

3 left

💡 Hint

Common Mistakes

Using ifft which computes the inverse FFT.

Using fftshift which shifts zero frequency component.

Using rfft which is for real input FFT.

The fft function computes the Fast Fourier Transform of a signal.

2fill in blank

medium

Complete the code to compute the inverse FFT of a frequency domain signal.

NumPy

import numpy as np
freq_signal = np.array([10+0j, -2+2j, -2+0j, -2-2j])
time_signal = np.[1](freq_signal)

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

Aifft

Brfft

Cfft

Dirfft

Attempts:

3 left

💡 Hint

Common Mistakes

Using fft which computes forward FFT.

Using rfft which is for real input FFT.

Using irfft which is inverse FFT for real input only.

The ifft function computes the inverse FFT, converting frequency domain back to time domain.

3fill in blank

hard

Fix the error in the code to compute the FFT of a signal using numpy.

NumPy

import numpy as np
signal = [1, 2, 3, 4]
fft_result = np.fft.[1](signal)

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

Afftshift

Bfft

Cifft

Drfft

Attempts:

3 left

💡 Hint

Common Mistakes

Using ifft instead of fft.

Using fftshift which only shifts the zero frequency component.

Using rfft which is for real input FFT but not the general FFT.

The correct function to compute FFT in numpy's fft module is fft.

4fill in blank

hard

Fill both blanks to create a dictionary of word lengths for words longer than 3 characters.

NumPy

words = ['data', 'science', 'ai', 'ml']
lengths = {word: [1] for word in words if len(word) [2] 3}

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

Alen(word)

Bword

C>

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using the word itself instead of its length.

Using the wrong comparison operator like <=.

The dictionary comprehension maps each word to its length if the word length is greater than 3.

5fill in blank

hard

Fill all three blanks to create a dictionary of uppercase words mapped to their lengths for words longer than 2 characters.

NumPy

words = ['fft', 'np', 'data', 'ai']
result = { [1]: [2] for word in words if len(word) [3] 2 }

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

Aword.upper()

Blen(word)

C>

Dword

Attempts:

3 left

💡 Hint

Common Mistakes

Using the original word instead of uppercase.

Using the wrong comparison operator like <.

The dictionary comprehension maps uppercase words to their lengths if the word length is greater than 2.

Practice

1. What does the np.fft.fft() function do in numpy?

easy

A. It calculates the mean of an array.

B. It sorts an array in ascending order.

C. It generates random numbers.

D. It computes the Fast Fourier Transform of a signal.

Solution

1. Step 1: Understand the purpose of FFT

   FFT converts time-domain data into frequency-domain data quickly.

2. Step 2: Identify the function role

   np.fft.fft() computes this Fast Fourier Transform on input data.

3. Final Answer:

   It computes the Fast Fourier Transform of a signal. -> Option D

4. Quick Check:

   FFT = Fast Fourier Transform [OK]

Hint: FFT = Fast Fourier Transform, converts time to frequency [OK]

Common Mistakes:

• Confusing FFT with sorting or averaging functions
• Thinking FFT generates random data
• Mixing FFT with statistical calculations

2. Which of the following is the correct syntax to compute the FFT of a numpy array data?

easy

A. np.fft(data).fft()

B. np.fft.fft(data)

C. fft(np.data)

D. np.fft_fft(data)

Solution

1. Step 1: Recall numpy FFT syntax

   The correct function call is np.fft.fft() with the data array as argument.

2. Step 2: Check each option

   Only np.fft.fft(data) matches the correct syntax; others are invalid or incorrect.

3. Final Answer:

   np.fft.fft(data) -> Option B

4. Quick Check:

   Correct function call = np.fft.fft(data) [OK]

Hint: Use np.fft.fft(array) to compute FFT [OK]

Common Mistakes:

• Swapping function and module order
• Using wrong function names
• Passing wrong argument types

3. What is the output of the following code?

import numpy as np
x = np.array([1, 0, 0, 0])
fft_x = np.fft.fft(x)
print(np.round(fft_x, 2))

medium

A. [1.+0.j 0.+0.j 0.+0.j 0.+0.j]

B. [1.+0.j 1.+0.j 1.+0.j 1.+0.j]

C. [4.+0.j 0.+0.j 0.+0.j 0.+0.j]

D. [0.+0.j 0.+0.j 0.+0.j 0.+0.j]

Solution

1. Step 1: Understand input signal

   The input array has one '1' followed by zeros, representing a unit impulse (delta function).

2. Step 2: Compute FFT of impulse

   The FFT of a unit impulse of length 4 is [4.+0.j 0.+0.j 0.+0.j 0.+0.j], because the sum of the input is 1 at position 0, but the FFT sums all elements, so the DC component is 4.

3. Final Answer:

   [4.+0.j 0.+0.j 0.+0.j 0.+0.j] -> Option C

4. Quick Check:

   Impulse FFT = DC component equals sum of input [OK]

Hint: FFT of unit impulse = all ones [Incorrect], actually FFT of [1,0,0,0] = [4,0,0,0] [OK]

Common Mistakes:

• Thinking FFT shows sum only at DC ([4.+0.j 0.+0.j 0.+0.j 0.+0.j])
• Ignoring complex number format
• Misreading array rounding

4. Identify the error in this code snippet:

import numpy as np
signal = [1, 2, 3, 4]
fft_signal = np.fft.fft(signal, n=-1)
print(fft_signal)

medium

A. The FFT length n cannot be smaller than the input length.

B. The print statement syntax is incorrect.

C. The function np.fft.fft does not accept the parameter n.

D. The input signal must be a numpy array, not a list.

Solution

1. Step 1: Check FFT length parameter

   The input signal length is 4, but n=-1 is smaller than input length.

2. Step 2: Understand FFT behavior with n parameter

   FFT length n must be at least the input length or zero-padded; smaller n truncates data causing error or unexpected results.

3. Final Answer:

   The FFT length n cannot be smaller than the input length. -> Option A

4. Quick Check:

   FFT length n ≥ input length [OK]

Hint: FFT length n ≥ input length [OK]

Common Mistakes:

• Thinking lists are invalid input
• Believing n can be any number
• Assuming print syntax error

5. You have a noisy signal stored in a numpy array noisy_signal. You want to remove high-frequency noise by zeroing FFT components above index 5. Which code correctly applies this filter and returns the cleaned signal?

hard

A. fft_vals = np.fft.fft(noisy_signal)
fft_vals[5:] = 0
clean_signal = np.fft.ifft(fft_vals).real

B. fft_vals = np.fft.fft(noisy_signal)
fft_vals[:5] = 0
clean_signal = np.fft.ifft(fft_vals).real

C. fft_vals = np.fft.ifft(noisy_signal)
fft_vals[5:] = 0
clean_signal = np.fft.fft(fft_vals).real

D. clean_signal = np.fft.fft(noisy_signal)
clean_signal[5:] = 0

Solution

1. Step 1: Compute FFT of noisy signal

   Use np.fft.fft(noisy_signal) to get frequency components.

2. Step 2: Zero out high-frequency components

   Set FFT values from index 5 onward to zero to remove high frequencies.

3. Step 3: Compute inverse FFT to get cleaned signal

   Apply np.fft.ifft() and take real part to get filtered time-domain signal.

4. Final Answer:

   fft_vals = np.fft.fft(noisy_signal) fft_vals[5:] = 0 clean_signal = np.fft.ifft(fft_vals).real -> Option A

5. Quick Check:

   Zero high freq FFT, then inverse FFT [OK]

Hint: Zero high freq FFT components, then inverse FFT [OK]

Common Mistakes:

• Zeroing low-frequency components instead
• Using ifft before fft
• Not taking real part after inverse FFT