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()

This is great for demonstration purposes! One thing I'm curious about; however, is that it appears that the frequency of the carrier is modulated by the slope of the base-band signal, rather than by it's amplitude. The max and min frequencies in the output signal appear to coincide with the PGT and NGT zeroes in the base-band signal. I was always under the impression it should be the opposite.

I'm also under the impression that the output signal is modulated by the slope of the base-band signal, rather than by it's amplitude, and think it should be the other way around 🤔

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))