FFT with np.fft module in NumPy

Introduction

FFT helps us quickly find the hidden frequencies in a signal. It turns time data into frequency data so we can understand patterns better.

Analyzing sound waves to find musical notes.

Checking vibrations in machines to detect problems.

Studying heartbeats to find irregular rhythms.

Finding repeating patterns in stock prices.

Syntax

NumPy

numpy.fft.fft(a, n=None, axis=-1, norm=None)

a is the input array (your signal data).

n is the length of the FFT (optional, pads or trims data).

Examples

Basic FFT on a small array of 4 numbers.

NumPy

import numpy as np
x = np.array([1, 2, 3, 4])
fft_result = np.fft.fft(x)

FFT with zero-padding to length 8 for higher frequency resolution.

NumPy

fft_result = np.fft.fft(x, n=8)

FFT along the first axis (default for 1D arrays).

NumPy

fft_result = np.fft.fft(x, axis=0)

Sample Program

This program creates a signal with two sine waves at 50 Hz and 120 Hz. It uses FFT to find these frequencies and prints their values and amplitudes. It also plots the original signal and the frequency spectrum.

NumPy

import numpy as np
import matplotlib.pyplot as plt

# Create a signal with two frequencies
sampling_rate = 1000  # samples per second
T = 1.0 / sampling_rate  # sample spacing
x = np.linspace(0.0, 1.0, sampling_rate, endpoint=False)
signal = 0.5 * np.sin(50.0 * 2.0 * np.pi * x) + 0.3 * np.sin(120.0 * 2.0 * np.pi * x)

# Compute FFT
fft_values = np.fft.fft(signal)

# Compute frequencies for x-axis
freqs = np.fft.fftfreq(len(signal), T)

# Take only the positive half of frequencies and amplitudes
positive_freqs = freqs[:len(freqs)//2]
positive_fft = np.abs(fft_values[:len(fft_values)//2])

# Print main frequency peaks
peak_indices = positive_fft.argsort()[-2:][::-1]
for i in peak_indices:
    print(f"Frequency: {positive_freqs[i]:.1f} Hz, Amplitude: {positive_fft[i]:.2f}")

# Plot the signal and its FFT
plt.subplot(2, 1, 1)
plt.plot(x, signal)
plt.title('Original Signal')
plt.xlabel('Time [s]')
plt.ylabel('Amplitude')

plt.subplot(2, 1, 2)
plt.stem(positive_freqs, positive_fft, use_line_collection=True)
plt.title('FFT Magnitude')
plt.xlabel('Frequency [Hz]')
plt.ylabel('Magnitude')
plt.tight_layout()
plt.show()

Important Notes

FFT output is complex numbers; use np.abs() to get amplitude.

Frequencies can be positive or negative; usually, we look at positive frequencies only.

Sampling rate affects frequency resolution and max frequency you can detect.

Summary

FFT converts time signals into frequency signals.

Use np.fft.fft() to perform FFT on data arrays.

Analyze the magnitude of FFT to find main frequencies in your data.