PM Modulation with Python: Code and Explanation

This article provides Python code for simulating Phase Modulation (PM) and Demodulation.

Introduction

Modulation falls into two primary categories: analog and digital.

• Analog Modulation: The baseband information or message signal is analog. Examples include AM, FM, and PM.
• Digital Modulation: The baseband information or message signal is digital (binary). Examples include ASK, FSK, and PSK.

PM, unlike PSK, utilizes an analog message signal. PSK modulation requires binary digital data as input.

The figure above illustrates the phase modulation process. As shown, an analog signal serves as the modulating or message (baseband) signal. This produces a PM modulated signal, where the RF carrier’s phase varies according to the positive or negative portions of the modulating sine wave. A positive half-cycle yields one phase, while a negative half-cycle yields another.

The following formula expresses the PM modulation process:

$e\_{PM} = A_c * sin[W_c*t + \Phi_m *sin(W_m*t)]$

PM Modulation and Demodulation Python Script

The following Python script generates PM modulated data and includes PM demodulation (implementation may vary depending on the specific demodulation technique).

# PM Modulation Python Script
import numpy as np
import matplotlib.pyplot as plt

# Define the modulation index (m) and the frequency of the carrier signal (fc)
m = 0.25
fc = 30

# Generate time values for the input signal
t = np.linspace(0, 1, 1000)

# Generate the input signal using a sinusoidal wave
input_signal = np.sin(2 * np.pi * 5 * t)
input_signal = input_signal.astype(int)

# Generate the carrier signal using a sinusoidal wave
carrier_signal = np.sin(2 * np.pi * fc * t)

# Calculate the phase change as per positive and negative cycles of the input signal
phase = np.zeros_like(t)
for i, val in enumerate(input_signal):
    if val >= 0:
        phase[i] = m * np.sin(2 * np.pi * 5 * t[i])
    else:
        phase[i] = -m * np.sin(2 * np.pi * 5 * t[i])

# Generate PM Modulated Signal
pm_modulated_signal = np.sin(2 * np.pi * fc * t + phase)

plt.subplot(3,1,1)
plt.plot(t, input_signal)
plt.title("Analog Message signal")
plt.subplot(3,1,2)
plt.plot(t, carrier_signal)
plt.title("RF carrier signal")
plt.subplot(3,1,3)
plt.plot(t, pm_modulated_signal)
plt.title("Phase Modulated Signal")
plt.tight_layout()
plt.show()

Output Plots

The script above produces the following plots: