FFT-based filtering in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

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

SciPy

import numpy as np
from scipy.fft import fft

signal = np.array([1, 2, 3, 4, 5])
fft_result = [1](signal)

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

Afftshift

Bifft

Crfft

Dfft

Attempts:

3 left

💡 Hint

Common Mistakes

Using ifft instead of fft will compute the inverse transform.

fftshift rearranges FFT output but does not compute FFT.

rfft computes FFT for real inputs but is not the general FFT function.

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

2fill in blank

medium

Complete the code to create a frequency mask that keeps frequencies below 10 Hz.

SciPy

import numpy as np
sampling_rate = 50  # Hz
n = 100
freqs = np.fft.fftfreq(n, d=1/sampling_rate)
mask = np.abs(freqs) [1] 10

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

A<

B>

C<=

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using >= or > will select frequencies above 10 Hz, which is incorrect.

Using <= includes 10 Hz exactly, which might be acceptable but the question asks for below 10.

The mask should select frequencies less than 10 Hz, so the operator is <.

3fill in blank

hard

Fix the error in the code to apply a low-pass filter using FFT.

SciPy

import numpy as np
from scipy.fft import fft, ifft

signal = np.sin(2 * np.pi * 5 * np.linspace(0, 1, 100)) + np.sin(2 * np.pi * 20 * np.linspace(0, 1, 100))
fft_signal = fft(signal)
freqs = np.fft.fftfreq(len(signal), d=1/100)
mask = np.abs(freqs) [1] 10
filtered_fft = fft_signal * mask
filtered_signal = ifft(filtered_fft).real

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

A<

B>

C>=

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using > or >= will keep high frequencies instead of low frequencies.

Using <= includes 10 Hz exactly, which might be acceptable but the question expects strictly less.

The mask should be True for frequencies less than 10 Hz to keep them, so use <.

4fill in blank

hard

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

SciPy

words = ['data', 'science', 'is', 'fun']
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 as value instead of its length.

Using <= instead of > will select shorter words.

We want the length of each word, so use len(word). We only want words longer than 3 characters, so use >.

5fill in blank

hard

Fill all three blanks to create a filtered dictionary of uppercase keys and values greater than 0.

SciPy

data = {'a': 1, 'b': -2, 'c': 3}
result = [1]: [2] for k, v in data.items() if v [3] 0

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

Ak.upper()

Bv

C>

Dk

Attempts:

3 left

💡 Hint

Common Mistakes

Using original keys without uppercase.

Filtering values less than or equal to zero.

Swapping keys and values.

The keys are converted to uppercase with k.upper(), values are v, and we filter values greater than 0 with >.

Practice

1. What is the main purpose of using FFT-based filtering in data analysis?

easy

A. To transform data into frequency domain for easier noise removal

B. To sort data values in ascending order

C. To calculate the average of data points

D. To convert data into text format

Solution

1. Step 1: Understand FFT transformation

   FFT converts data from time domain to frequency domain, revealing frequency components.

2. Step 2: Purpose of filtering in frequency domain

   Filtering in frequency domain allows easy removal of unwanted noise or frequencies.

3. Final Answer:

   To transform data into frequency domain for easier noise removal -> Option A

4. Quick Check:

   FFT filtering = frequency domain noise removal [OK]

Hint: FFT helps remove noise by working in frequency domain [OK]

Common Mistakes:

• Confusing FFT with sorting or averaging
• Thinking FFT changes data to text
• Assuming FFT directly cleans data without filtering

2. Which of the following is the correct way to compute the FFT of a 1D numpy array data using scipy?

easy

A. fft_data = scipy.fft_transform(data)

B. fft_data = scipy.fft(data)

C. fft_data = scipy.fft.fft(data)

D. fft_data = scipy.fft_fft(data)

Solution

1. Step 1: Identify correct scipy FFT function

   The scipy FFT module uses fft() to compute the Fast Fourier Transform.

2. Step 2: Check syntax correctness

   The correct syntax is scipy.fft.fft(data), other options are invalid function names.

3. Final Answer:

   fft_data = scipy.fft.fft(data) -> Option C

4. Quick Check:

   Correct FFT call = scipy.fft.fft(data) [OK]

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

Common Mistakes:

• Using incorrect function names like fft_transform
• Omitting the .fft part after scipy.fft
• Confusing with numpy.fft functions

3. Given the code below, what will be the output of filtered_signal?

import numpy as np
from scipy.fft import fft, ifft

data = np.array([1, 2, 3, 4])
fft_data = fft(data)
mask = np.array([1, 0, 0, 1])
filtered_fft = fft_data * mask
filtered_signal = ifft(filtered_fft).real
print(np.round(filtered_signal, 2))

medium

A. [1. 0. 0. 4.]

B. [2. 2. 3. 3.]

C. [1.5 0. 0. 3.5]

D. [2. 0. 0. 2.]

Solution

1. Step 1: Compute FFT and apply mask

   FFT of data is computed, then multiplied by mask [1,0,0,1], zeroing middle frequencies.

2. Step 2: Compute inverse FFT and round

   Inverse FFT of masked data gives filtered signal; rounding to 2 decimals yields [2. 0. 0. 2.].

3. Final Answer:

   [2. 0. 0. 2.] -> Option D

4. Quick Check:

   Mask zeros middle frequencies, inverse FFT smooths signal [OK]

Hint: Mask zeros frequencies, inverse FFT returns filtered signal [OK]

Common Mistakes:

• Forgetting to multiply FFT by mask
• Not taking real part after inverse FFT
• Rounding incorrectly or not at all

4. Identify the error in the following FFT-based filtering code snippet:

import numpy as np
from scipy.fft import fft, ifft

data = np.array([1, 2, 3, 4])
fft_data = fft(data)
mask = np.array([1, 0, 0])
filtered_fft = fft_data * mask
filtered_signal = ifft(filtered_fft).real
print(filtered_signal)

medium

A. Data array should be complex type

B. Mask length does not match FFT data length

C. Using ifft instead of fft

D. Missing import for numpy

Solution

1. Step 1: Check mask and FFT data lengths

   FFT of data has length 4, but mask length is 3, causing shape mismatch error.

2. Step 2: Identify error cause

   Multiplying arrays of different lengths raises an error; mask must match FFT length.

3. Final Answer:

   Mask length does not match FFT data length -> Option B

4. Quick Check:

   Mask length must equal FFT length [OK]

Hint: Mask length must match FFT output length [OK]

Common Mistakes:

• Using mask shorter than FFT result
• Confusing ifft with fft usage
• Assuming data must be complex initially

5. You have a noisy signal sampled at 1000 Hz stored in signal. You want to remove frequencies above 100 Hz using FFT-based filtering. Which code snippet correctly implements this filter?

hard

A. import numpy as np
from scipy.fft import fft, ifft
N = len(signal)
freqs = np.fft.fftfreq(N, 1/1000)
fft_signal = fft(signal)
mask = np.abs(freqs) <= 100
filtered_fft = fft_signal * mask
filtered_signal = ifft(filtered_fft).real

B. import numpy as np
from scipy.fft import fft, ifft
N = len(signal)
freqs = np.fft.fftfreq(N)
fft_signal = fft(signal)
mask = freqs < 100
filtered_fft = fft_signal * mask
filtered_signal = ifft(filtered_fft).real

C. import numpy as np
from scipy.fft import fft, ifft
N = len(signal)
freqs = np.fft.fftfreq(N, 1/1000)
fft_signal = fft(signal)
mask = freqs > 100
filtered_fft = fft_signal * mask
filtered_signal = ifft(filtered_fft).real

D. import numpy as np
from scipy.fft import fft, ifft
N = len(signal)
freqs = np.fft.fftfreq(N, 1/1000)
fft_signal = fft(signal)
mask = np.abs(freqs) >= 100
filtered_fft = fft_signal * mask
filtered_signal = ifft(filtered_fft).real

Solution

1. Step 1: Calculate frequency bins correctly

   Use np.fft.fftfreq(N, 1/1000) to get frequencies in Hz for sampling rate 1000 Hz.

2. Step 2: Create mask to keep frequencies ≤ 100 Hz

   Mask should be np.abs(freqs) <= 100 to keep low frequencies and remove higher ones.

3. Step 3: Apply mask and inverse FFT

   Multiply FFT by mask, then apply inverse FFT and take real part for filtered signal.

4. Final Answer:

   mask = np.abs(freqs) <= 100 with freqs = np.fft.fftfreq(N, 1/1000) -> Option A

5. Quick Check:

   Mask keeps frequencies ≤ 100 Hz [OK]

Hint: Use np.abs(freqs) ≤ cutoff for low-pass mask [OK]

Common Mistakes:

• Ignoring sampling rate in frequency calculation
• Using wrong comparison operators in mask
• Not taking absolute value of frequencies