SciPy — FFT

Basic FFT

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

x = np.array([0, 1, 2, 3, 4, 5])
y = fft(x)
print(f"FFT: {y}")
print(f"Inverse FFT: {ifft(y).real}")

2D FFT

from scipy.fft import fft2, ifft2

x = np.array([[1, 2], [3, 4]])
y = fft2(x)
print(f"2D FFT:\n{y}")

FFT frequencies

from scipy.fft import fftfreq

n = 100
T = 1.0 / 100.0
freqs = fftfreq(n, T)
print(f"Frequencies: {freqs[:n//2]}")

Signal analysis

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

# Create signal
t = np.linspace(0, 1, 1000)
signal = np.sin(2 * np.pi * 50 * t) + 0.5 * np.sin(2 * np.pi * 120 * t)

# Compute FFT
yf = fft(signal)
xf = fftfreq(len(t), t[1] - t[0])

# Find peaks
positive_mask = xf > 0
frequencies = xf[positive_mask]
magnitudes = 2.0/len(t) * np.abs(yf[positive_mask])

Windowing

from scipy.signal import windows

# Hanning window
window = windows.hann(100)
windowed_signal = signal * window

Applications

• Audio processing
• Image filtering
• Signal analysis
• Spectrum analysis

Mini Practice

1. Compute FFT of a signal
2. Find frequency components
3. Apply windowing
4. Reconstruct signal from FFT

Up Next

Continue with Signal Processing - Signal analysis.