Frequency array generation (fftfreq) in SciPy

Introduction

We use frequency arrays to understand the different frequency parts in a signal. This helps us analyze patterns like sound waves or vibrations.

When you want to find the frequencies present in a time-based signal like audio.

When analyzing sensor data to detect repeating patterns or cycles.

When preparing data for a Fourier Transform to see frequency components.

When filtering signals by frequency to remove noise or unwanted parts.

Syntax

SciPy

from scipy.fft import fftfreq

# n: number of points
# d: sample spacing (time between samples)
frequencies = fftfreq(n, d)

n is how many data points you have.

d is the time gap between each data point, like how often you measure.

Examples

This creates frequencies for 4 samples taken every 1 second.

SciPy

from scipy.fft import fftfreq

# Example 1: 4 points, sample spacing 1 second
frequencies = fftfreq(4, 1)
print(frequencies)

Here, 5 samples are taken every half second, so frequencies adjust accordingly.

SciPy

from scipy.fft import fftfreq

# Example 2: 5 points, sample spacing 0.5 seconds
frequencies = fftfreq(5, 0.5)
print(frequencies)

Edge case: only one data point, frequency array will have one zero.

SciPy

from scipy.fft import fftfreq

# Example 3: 1 point, sample spacing 1 second
frequencies = fftfreq(1, 1)
print(frequencies)

Edge case: no data points, frequency array is empty.

SciPy

from scipy.fft import fftfreq

# Example 4: 0 points (empty), sample spacing 1 second
frequencies = fftfreq(0, 1)
print(frequencies)

Sample Program

This program creates a frequency array for 6 data points sampled every 0.2 seconds. It prints the number of points, sample spacing, and the resulting frequency array.

SciPy

from scipy.fft import fftfreq

# Number of data points
number_of_points = 6

# Sample spacing in seconds
sample_spacing = 0.2

# Generate frequency array
frequency_array = fftfreq(number_of_points, sample_spacing)

print(f"Number of points: {number_of_points}")
print(f"Sample spacing: {sample_spacing} seconds")
print("Frequency array:")
print(frequency_array)

Important Notes

The time complexity of fftfreq is O(n), where n is the number of points.

The space complexity is O(n) because it returns an array of length n.

A common mistake is forgetting to set the correct sample spacing d, which changes the frequency scale.

Use fftfreq when you want the frequency bins for Fourier Transform results. For other frequency calculations, different methods may be needed.

Summary

Frequency arrays help us map data points to their frequency values.

fftfreq needs the number of points and sample spacing to work.

It returns an array showing positive and negative frequencies for analysis.