Frequency array generation (fftfreq) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the fftfreq function from scipy.fft module.

SciPy

from scipy.fft import [1]

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

Afft

Bfftshift

Cifft

Dfftfreq

Attempts:

3 left

💡 Hint

Common Mistakes

Importing 'fft' instead of 'fftfreq'.

Using 'ifft' which is inverse FFT.

Importing 'fftshift' which shifts zero frequency.

The fftfreq function is imported from scipy.fft to generate frequency bins for FFT.

2fill in blank

medium

Complete the code to generate frequency bins for a signal of length 8.

SciPy

freqs = fftfreq([1])

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

A8

B16

C4

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Using a number larger or smaller than the signal length.

Confusing frequency bins count with sampling rate.

The length of the signal is 8, so fftfreq(8) generates 8 frequency bins.

3fill in blank

hard

Fix the error in the code to generate frequency bins with a sample spacing of 0.5 seconds.

SciPy

freqs = fftfreq(10, [1]=0.5)

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

Ad

Bdt

Cspacing

Dsample_spacing

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'dt' or 'spacing' which are not valid parameter names.

Passing sample spacing as a positional argument instead of keyword.

The correct parameter name for sample spacing in fftfreq is d.

4fill in blank

hard

Fill both blanks to create a frequency array for 12 samples with sample spacing 0.1 seconds.

SciPy

freqs = fftfreq([1], [2]=0.1)

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

A12

B10

Cd

Ddt

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong parameter name for sample spacing.

Using incorrect number of samples.

The first argument is the number of samples (12), and the sample spacing parameter is d.

5fill in blank

hard

Fill all three blanks to create a dictionary mapping frequencies to their indices for 6 samples with spacing 0.2 seconds, including only positive frequencies.

SciPy

freqs = fftfreq([1], [2]=0.2)
positive_freqs = {i: f for i, f in enumerate(freqs) if f [3] 0}

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

A6

Bd

C>

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong comparison operator to filter frequencies.

Using incorrect parameter name for sample spacing.

Using wrong number of samples.

We use 6 samples, sample spacing parameter d, and filter frequencies greater than zero.

Practice

1. What does the scipy.fft.fftfreq function return when given the number of points and sample spacing?

easy

A. A random array of the same length as input

B. The Fourier transform of the input data

C. The inverse Fourier transform of the input data

D. An array of frequency bins corresponding to the FFT output

Solution

1. Step 1: Understand the purpose of fftfreq

   The fftfreq function generates frequency bins for FFT results, not the transform itself.

2. Step 2: Identify the output type

   It returns an array of frequencies that correspond to FFT output indices, including positive and negative frequencies.

3. Final Answer:

   An array of frequency bins corresponding to the FFT output -> Option D

4. Quick Check:

   fftfreq returns frequency bins [OK]

Hint: fftfreq gives frequency bins, not the transform itself [OK]

Common Mistakes:

• Confusing fftfreq output with FFT transform
• Expecting only positive frequencies
• Thinking it returns time domain data

2. Which of the following is the correct way to import and use fftfreq from scipy to generate frequency bins for 8 points with sample spacing 0.5?

easy

A. from scipy import fftfreq
freqs = fftfreq(8, 0.5)

B. import scipy.fft
freqs = scipy.fft.fftfreq(0.5, 8)

C. from scipy.fft import fftfreq
freqs = fftfreq(8, 0.5)

D. import fftfreq from scipy.fft
freqs = fftfreq(8, 0.5)

Solution

1. Step 1: Check the correct import syntax

   The correct import is from scipy.fft import fftfreq, not directly from scipy or using wrong syntax.

2. Step 2: Verify function parameters order

   fftfreq takes number of points first, then sample spacing, so fftfreq(8, 0.5) is correct.

3. Final Answer:

   from scipy.fft import fftfreq freqs = fftfreq(8, 0.5) -> Option C

4. Quick Check:

   Correct import and parameter order [OK]

Hint: Import from scipy.fft and pass (n, d) in order [OK]

Common Mistakes:

• Swapping parameters order
• Wrong import statement
• Using scipy.fftfreq instead of scipy.fft.fftfreq

3. What is the output of the following code?

from scipy.fft import fftfreq
freqs = fftfreq(4, 1.0)
print(freqs)

medium

A. [0.0, 0.5, -0.5, -0.25]

B. [0.0, 0.25, -0.5, -0.25]

C. [0.0, 0.25, 0.5, 0.75]

D. [0.0, 0.5, 1.0, 1.5]

Solution

1. Step 1: Understand fftfreq output for n=4, d=1.0

   For 4 points, frequencies are [0, 1/4, -2/4, -1/4] = [0.0, 0.25, -0.5, -0.25].

2. Step 2: Confirm printed array matches expected frequencies

   The printed array matches [0.0, 0.25, -0.5, -0.25] exactly.

3. Final Answer:

   [0.0, 0.25, -0.5, -0.25] -> Option B

4. Quick Check:

   fftfreq(4,1.0) = [0, 0.25, -0.5, -0.25] [OK]

Hint: For even n, negative freqs start at -n/2/n [OK]

Common Mistakes:

• Ignoring negative frequencies
• Miscomputing frequency steps
• Confusing sample spacing effect

4. The code below throws an error. What is the cause and how to fix it?

from scipy import fftfreq
freqs = fftfreq(5)
print(freqs)

medium

A. Import statement is incorrect; use import scipy.fft instead

B. fftfreq requires input data array, not just number of points

C. Missing sample spacing argument; add a second argument like 1.0

D. fftfreq cannot handle odd number of points

Solution

1. Step 1: Identify the cause of the error

   The import from scipy import fftfreq fails because fftfreq is in the scipy.fft submodule.

2. Step 2: Fix by using correct import

   Change to from scipy.fft import fftfreq or import scipy.fft and call scipy.fft.fftfreq(5).

3. Final Answer:

   Import statement is incorrect; use import scipy.fft instead -> Option A

4. Quick Check:

   fftfreq requires scipy.fft import [OK]

Hint: fftfreq is in scipy.fft submodule [OK]

Common Mistakes:

• Importing fftfreq directly from scipy
• Confusing fftfreq with fft function
• Wrong import causing unrelated errors

5. You have a signal sampled at 10 Hz with 10 data points. Using fftfreq, how do you generate the frequency bins array? What is the frequency value at index 3?

hard

A. freqs = fftfreq(10, 0.1); frequency at index 3 is 3 Hz

B. freqs = fftfreq(10, 0.1); frequency at index 3 is 0.3 Hz

C. freqs = fftfreq(10, 10); frequency at index 3 is 3 Hz

D. freqs = fftfreq(10, 1); frequency at index 3 is 0.3 Hz

Solution

1. Step 1: Calculate sample spacing from sampling rate

   Sampling rate is 10 Hz, so sample spacing d = 1/10 = 0.1 seconds.

2. Step 2: Use fftfreq with n=10 and d=0.1

   Calling fftfreq(10, 0.1) generates frequencies: [0, 1, 2, 3, 4, -5, -4, -3, -2, -1] Hz.

3. Step 3: Identify frequency at index 3

   Frequency step df = 1/(n*d) = 1 Hz, so index 3 is 3 Hz.

4. Final Answer:

   freqs = fftfreq(10, 0.1); frequency at index 3 is 3 Hz -> Option A

5. Quick Check:

   Sample spacing = 0.1, freq[3] = 3 Hz [OK]

Hint: Sample spacing = 1 / fs; freq[k] = k / (n * d) [OK]

Common Mistakes:

• Using sampling rate as spacing directly
• Mixing up index and frequency value
• Incorrect parameter order in fftfreq