Why Fourier transforms reveal frequencies in SciPy - See It in Action

Why Fourier transforms reveal frequencies

📖 Scenario: Imagine you recorded a sound that is a mix of two musical notes played together. You want to find out which notes (frequencies) are in the sound.

🎯 Goal: You will create a simple signal with two frequencies, use Fourier transform to find these frequencies, and then display the result.

📋 What You'll Learn

Create a time array for the signal

Create a signal with two sine waves of different frequencies

Use Fourier transform to find frequency components

Print the frequencies found in the signal

💡 Why This Matters

🌍 Real World

Fourier transforms help us find hidden frequencies in signals like music, sound, or sensor data.

💼 Career

Data scientists use Fourier analysis in fields like audio processing, communications, and vibration analysis.

1

Create a time array for the signal

Create a variable called t that is a numpy array of 500 points evenly spaced from 0 to 1 second.

SciPy

import numpy as np
# Create the time array t with 500 points from 0 to 1
# Your code here

Need a hint?

Use np.linspace(0, 1, 500) to create the time array.

2

Create a signal with two sine waves

Create a variable called signal that is the sum of two sine waves: one with frequency 5 Hz and one with frequency 20 Hz, both using the time array t. Use np.sin() and multiply the frequency by 2 * np.pi * t.

SciPy

import numpy as np

t = np.linspace(0, 1, 500)
# Create signal as sum of 5 Hz and 20 Hz sine waves
# Your code here

Need a hint?

Use np.sin(2 * np.pi * frequency * t) for each sine wave and add them.

3

Apply Fourier transform to find frequencies

Import fft and fftfreq from scipy.fft. Create a variable called fft_values by applying fft to signal. Create a variable called frequencies by applying fftfreq to the length of signal and the sample spacing 1/500.

SciPy

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

t = np.linspace(0, 1, 500)
signal = np.sin(2 * np.pi * 5 * t) + np.sin(2 * np.pi * 20 * t)
# Compute fft_values and frequencies
# Your code here

Need a hint?

Use fft(signal) and fftfreq(len(signal), 1/500) to get frequency components.

4

Print the main frequencies found

Print the frequencies where the absolute value of fft_values is greater than 100. Use a for loop with variables freq and value iterating over zip(frequencies, fft_values). Print freq rounded to 1 decimal place.

SciPy

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

t = np.linspace(0, 1, 500)
signal = np.sin(2 * np.pi * 5 * t) + np.sin(2 * np.pi * 20 * t)

fft_values = fft(signal)
frequencies = fftfreq(len(signal), 1/500)
# Print frequencies with large fft_values
# Your code here

Need a hint?

Check absolute fft values and print frequencies where value is large.