Why Fourier transforms reveal frequencies in SciPy - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the Fourier transform function from scipy.

SciPy

from scipy.fft import [1]

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

Afft

Bsin

Ccos

Dintegrate

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'sin' or 'cos' instead of 'fft' because they are trigonometric functions, not transform functions.

Trying to import 'integrate' which is unrelated here.

The fft function computes the Fast Fourier Transform, which reveals frequency components.

2fill in blank

medium

Complete the code to create a time array from 0 to 1 second with 500 points.

SciPy

import numpy as np
time = np.linspace(0, [1], 500)

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

A100

B1

C0.1

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Using 10 or 100 which are too large for 1 second duration.

Using 0.1 which is too short.

The time array should span 1 second, so the end value is 1.

3fill in blank

hard

Fix the error in the code to generate a signal with frequency 5 Hz.

SciPy

freq = 5
signal = np.sin(2 * np.pi * freq * [1])

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

Anp.pi

Bfreq

Cnp.linspace

Dtime

Attempts:

3 left

💡 Hint

Common Mistakes

Using frequency variable instead of time inside the sine function.

Using np.linspace which is a function, not a variable.

The signal depends on time, so the variable time must be used inside the sine function.

4fill in blank

hard

Fill both blanks to compute the Fourier transform and get the frequency bins.

SciPy

yf = [1](signal)
xf = np.fft.fftfreq(len(signal), [2])

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

Afft

B0.002

C0.01

Dsin

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'sin' instead of 'fft' for the transform.

Using wrong sample spacing like 0.01 which does not match 500 points per second.

fft computes the Fourier transform. The second blank is the sample spacing, which is 1/500 = 0.002 seconds.

5fill in blank

hard

Fill both blanks to create a dictionary of frequencies and their amplitudes above a threshold.

SciPy

result = {xf[1]: abs(yf) for i, yf in enumerate(yf) if abs(yf) [2] 10}

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

A[i]

B>

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using parentheses instead of square brackets for indexing.

Using less than instead of greater than for filtering.

The frequency at index i is xf[i]. The amplitude is abs(yf). We filter amplitudes greater than 10.