Frequency modulation Python matplotlib visualisation

frequency_modulation_visualisation.py

import numpy as np
import matplotlib.pyplot as plt

modulator_frequency = 4.0
carrier_frequency = 40.0
modulation_index = 1.0

time = np.arange(44100.0) / 44100.0
modulator = np.sin(2.0 * np.pi * modulator_frequency * time) * modulation_index
carrier = np.sin(2.0 * np.pi * carrier_frequency * time)
product = np.zeros_like(modulator)

for i, t in enumerate(time):
    product[i] = np.sin(2. * np.pi * (carrier_frequency * t + modulator[i]))

plt.subplot(3, 1, 1)
plt.title('Frequency Modulation')
plt.plot(modulator)
plt.ylabel('Amplitude')
plt.xlabel('Modulator signal')
plt.subplot(3, 1, 2)
plt.plot(carrier)
plt.ylabel('Amplitude')
plt.xlabel('Carrier signal')
plt.subplot(3, 1, 3)
plt.plot(product)
plt.ylabel('Amplitude')
plt.xlabel('Output signal')
plt.show()

Anyone looking up the code,

1. Remove the 2.0 * np.pi parts as it is unnecessary

2. change product[i] = np.sin(2. * np.pi * (carrier_frequency * t + modulator[i]))
   to
   product[i] = np.sin(carrier_frequency * time - modulation_index * np.cos(modulator_frequency * time))