How can I visualize FFT results using NumPy?

How can I visualize FFT results using NumPy?

You can use libraries like Matplotlib to visualize the FFT results. First, compute the FFT using NumPy, then plot the magnitude spectrum.

Can you show me a code example for that?

Sure! Here's a simple example:

import numpy as np
import matplotlib.pyplot as plt

# Sample signal
fs = 1000  # Sampling frequency
T = 1.0 / fs  # Sampling interval
x = np.linspace(0.0, 1.0, fs)
y = np.sin(2.0 * np.pi * 50.0 * x) + 0.5 * np.sin(2.0 * np.pi * 120.0 * x)

# Compute FFT
yf = np.fft.fft(y)
xf = np.fft.fftfreq(len(y), T)[:len(y)//2]

# Plotting
plt.plot(xf, 2.0/len(y) * np.abs(yf[:len(y)//2]))
plt.grid()
plt.title('FFT of the signal')
plt.xlabel('Frequency (Hz)')
plt.ylabel('Magnitude')
plt.show()

What if I want to visualize the phase spectrum as well?

You can plot the phase spectrum using np.angle() on the FFT results. Here's how you can modify the code:

# Plotting phase spectrum
plt.figure()
plt.plot(xf, np.angle(yf[:len(y)//2]))
plt.grid()
plt.title('Phase Spectrum')
plt.xlabel('Frequency (Hz)')
plt.ylabel('Phase (radians)')
plt.show()