Amplitude, Frequency, and Phase Modulation Techniques

📘 Overview
🧮 Amplitude Modulation (AM)
🧮 Online Amplitude Modulation Simulator
🧮 MATLAB Code for AM
🧮 Frequency Modulation (FM)
🧮 MATLAB Code for FM
🧮 Phase Modulation (PM)
🧮 MATLAB Codes
📚 Further Reading

1. Analog Modulation Techniques:

Now we'll discuss some analog modulation techniques for bandpass signals, including amplitude modulation, frequency modulation, and phase modulation.

1.1.1. Amplitude Modulation (AM):

The carrier signal's amplitude varies linearly with the amplitude of the message signal.

An AM wave may thus be described, in the most general form, as a function of time as follows.

When performing amplitude modulation (AM) with a carrier frequency of 100 Hz and a message frequency of 10 Hz, the resulting peak frequencies are as follows: 90 Hz (100 - 10 Hz), 100 Hz, and 110 Hz (100 + 10 Hz).

Figure: Frequency Spectrums of AM Signal (Lower Sideband, Carrier, and Upper Sideband)

A low-frequency message signal is modulated with a high-frequency carrier wave using a local oscillator to make communication possible. DSB, SSB, and VSB are common amplitude modulation techniques. We find a lot of bandwidth loss in DSB. The bandwidth of SSB is half that of DSB. Because of its low bandwidth, SSB is ideal for audio transmission. VSB has a little higher bandwidth than SSB, making it appropriate for video transmission.

MATLAB Code for Amplitude Modulation

% The code is written by SalimWireless.Com 
% Amplitude Modulation (AM) and Demodulation
clc;
clear all;
close all;

% Define parameters
carrier_frequency = 100;      % Carrier frequency in Hertz
message_frequency = 10;       % Message signal frequency in Hertz
sampling_frequency = 10 * carrier_frequency; % Sampling frequency in Hertz
time = 0:1/sampling_frequency:1; % Time vector

% Generate the message signal (a sine wave)
message_signal = sin(2 * pi * message_frequency * time);

% Generate the carrier signal (a cosine wave)
carrier_signal = cos(2 * pi * carrier_frequency * time);

% Perform Amplitude Modulation (AM)
am_signal = (1 + 0.5 * message_signal) .* carrier_signal;

% Plot the signals
subplot(3,1,1);
plot(time, message_signal);
title('Message Signal');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(3,1,2);
plot(time, carrier_signal);
title('Carrier Signal');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(3,1,3);
plot(time, am_signal);
title('Amplitude Modulated Signal');
xlabel('Time (s)');
ylabel('Amplitude');

% Perform Amplitude Demodulation
demodulated_signal = am_signal .* carrier_signal;

% Apply low-pass filter to remove high-frequency components
cutoff_frequency = 2 * message_frequency;
[b, a] = butter(6, cutoff_frequency / (sampling_frequency/2), 'low');
demodulated_signal_filtered = filtfilt(b, a, demodulated_signal);

% Plot the demodulated signal
figure;
plot(time, demodulated_signal_filtered);
title('Demodulated and Filtered Signal');
xlabel('Time (s)');
ylabel('Amplitude');
web('https://www.salimwireless.com/search?q=modulation%20techniques', '-browser');

Output

Fig 1: Amplitude Modulation and Demodulation

1.1.2. Frequency Modulation (FM):

The carrier signal's frequency varies linearly in response to the voltage variation in the message signal.

Here, modulation index = Δf / fm

Where Δf is the peak frequency deviation and fm = frequency of the message signal.

Here frequency deviation means how much the the frequency of the carrier signal deviates from its carrier's original frequency after frequency modulation.

When performing frequency modulation (FM) with a carrier frequency of 100 Hz and a message frequency of 10 Hz, the resulting peak frequencies are as follows: 80 Hz (100 - 2*10 Hz), 90 Hz (100 - 10 Hz), 100 Hz, 110 Hz (100 + 10 Hz), 120 Hz (100 + 2*10 Hz).

Figure: Frequency Spectrums of FM Signal

MATLAB Code for Frequency Modulation and Demodulation

% The code is written by SalimWireless.Com 
% Frequency Modulation (FM) and Demodulation
clc;
clear all;
close all;
function Frequency_Modulation_Paraphrased
    % Parameters for Frequency Modulation

% Carrier frequency
    carrier_frequency = 100;

% Message signal frequency
    message_frequency = 10;

% Amplitude of the message signal
    message_amplitude = 1;

% Frequency sensitivity (modulation index)
    sensitivity = 50;

% Sampling frequency
    sampling_frequency = 10 * max(carrier_frequency, message_frequency);

% Time vector from 0 to 1 second
    time_vector = 0:1/sampling_frequency:1;

% Generate the message signal
    message_signal = message_amplitude * cos(2*pi*message_frequency*time_vector);

% FM modulation
    modulated_signal = my_fmmod(message_signal, carrier_frequency, sampling_frequency, sensitivity);

% Plot original message signal and the modulated signal
    plot_signals(time_vector, message_signal, modulated_signal);

% Coherent Frequency Demodulation (FM)
    demodulated_signal = my_coherent_fmdemod(modulated_signal, carrier_frequency, sampling_frequency, sensitivity, time_vector, message_frequency);

% Plot the demodulated signal
    plot_demodulated_signal(time_vector, demodulated_signal);
end

function modulated_signal = my_fmmod(message_signal, carrier_frequency, sampling_frequency, sensitivity)
    % Function to perform FM modulation

% Generate the time vector
    time_vector = 0:1/sampling_frequency:(length(message_signal)-1)/sampling_frequency;

% Calculate phase deviation based on the message signal
    phase_deviation = sensitivity * cumsum(message_signal) * 2*pi/sampling_frequency;

% Modulate the signal using FM modulation
    modulated_signal = cos(2*pi*carrier_frequency*time_vector + phase_deviation);

% Scale the modulated signal to match the amplitude of the message signal
    modulated_signal = scale_amplitude(message_signal, modulated_signal);
end

function scaled_signal = scale_amplitude(original_signal, signal_to_scale)
    % Function to scale the amplitude of a signal

% Calculate the amplitude ratio between the original and scaled signals
    amplitude_ratio = rms(original_signal) / rms(signal_to_scale);

% Scale the signal_to_scale to match the amplitude of the original_signal
    scaled_signal = amplitude_ratio * signal_to_scale;
end

function demodulated_signal = my_coherent_fmdemod(modulated_signal, carrier_frequency, sampling_frequency, sensitivity, time_vector, message_frequency)
    % Function to perform coherent frequency demodulation (FM)

% Generate the local oscillator signal
    local_oscillator = cos(2*pi*carrier_frequency*time_vector);

% Demodulate the modulated signal using the local oscillator
    demodulated_signal = modulated_signal .* local_oscillator;

% Apply a low-pass filter (Butterworth filter) to remove high-frequency components
    demodulated_signal = apply_low_pass_filter(demodulated_signal, sampling_frequency, message_frequency);
end

function filtered_signal = apply_low_pass_filter(signal, sampling_frequency, cutoff_frequency)
    % Function to apply a low-pass filter (Butterworth filter)

% Set filter parameters
    filter_order = 4; % Order of the Butterworth filter
    cutoff_frequency = cutoff_frequency * 1.5; % Adjust the cutoff frequency as needed

% Design the Butterworth filter
    [b, a] = butter(filter_order, cutoff_frequency/(sampling_frequency/2), 'low');

% Apply the filter to the signal
    filtered_signal = filtfilt(b, a, signal);
end

function plot_signals(time_vector, message_signal, modulated_signal)
    % Function to plot the original message signal and the modulated signal

% Plot the original message signal
    subplot(2,1,1);
    plot(time_vector, message_signal);
    title('Message Signal');
    xlabel('Time (s)');
    ylabel('Amplitude');

% Plot the modulated signal
    subplot(2,1,2);
    plot(time_vector, modulated_signal);
    title('FM Modulated Signal');
    xlabel('Time (s)');
    ylabel('Amplitude');
end

function plot_demodulated_signal(time_vector, demodulated_signal)
    % Function to plot the demodulated signal

% Plot the demodulated signal
    figure;
    plot(time_vector, demodulated_signal);
    title('Demodulated Signal (Coherent FM)');
    xlabel('Time (s)');
    ylabel('Amplitude');
end

Output

Fig 2: Frequency Modulation and Demodulation

1.1.3. Phase Modulation (PM):

In phase modulation, the phase of the carrier signal varies linearly in accordance with the message signal voltage.

Where, s(t) is the carrier signal and m(t) is the message signal.

Here in the above equation Kp is the phase sensitivity; the phase of the carrier signal signal is varied in accordance to the amplitude of the message signal where the amplitude of the carrier remain same in the modulation process.

In the phase modulation process,

the modulation index = ΔΦ / fm.T

where, ΔΦ is the peak frequency deviation representing the maximum change in carrier frequency due to modulation

fm and T are the frequency and the period of the message signal respectively

MATLAB Code for Phase Modulation and Demodulation

% The code is written by SalimWireless.Com 
% Phase Modulation (PM) and Demodulation
clc;
clear all;
close all;
function PhaseModulationExample
    % Parameters
    fs = 1000;          % Sampling frequency (Hz)
    fc = 100;           % Carrier frequency (Hz)
    fm = 5;             % Message signal frequency (Hz)
    phasedev = pi/2;    % Phase deviation

% Time vector
    t = 0:1/fs:1;

% Generate message signal
    message_signal = cos(2*pi*fm*t);

% Phase modulation
    modulated_signal = pmmod(message_signal, fc, fs, phasedev);

% Phase demodulation with alternative low-pass filter
    demodulated_signal = pmdemod(modulated_signal, fc, fs, phasedev);

% Plot the original message signal, modulated signal, and demodulated signal
    figure;

subplot(3,1,1);
    plot(t, message_signal);
    title('Original Message Signal');
    xlabel('Time (s)');
    ylabel('Amplitude');

subplot(3,1,2);
    plot(t, modulated_signal);
    title('Phase Modulated Signal');
    xlabel('Time (s)');
    ylabel('Amplitude');

subplot(3,1,3);
    plot(t, demodulated_signal);
    title('Demodulated Signal with Alternative Low-pass Filter');
    xlabel('Time (s)');
    ylabel('Amplitude');
end

% Phase modulation function
function y = pmmod(x, Fc, Fs, phasedev)
    t = 0:1/Fs:(length(x)-1)/Fs;
    y = cos(2*pi*Fc*t + phasedev*x);
end

% Phase demodulation function with alternative low-pass filter
function z = pmdemod(y, Fc, Fs, phasedev)
    t = 0:1/Fs:(length(y)-1)/Fs;
    y_analytic = hilbert(y);
    instantaneous_phase = unwrap(angle(y_analytic));
    demodulated_signal = gradient(instantaneous_phase) / (2*pi*Fc/Fs);
    z = phasedev * demodulated_signal;

% Apply an alternative low-pass filter
    cutoff_frequency = 5;  % Adjust the cutoff frequency as needed
    filter_order = 8;      % Adjust the filter order as needed

% Design a low-pass FIR filter using fir1
    b = fir1(filter_order, cutoff_frequency/(Fs/2), 'low');

% Apply the filter using filtfilt for zero-phase filtering
    z = filtfilt(b, 1, z);
end

Output

Also Read about

2. Digital Modulation Techniques:

Examples of digital modulation techniques are ASK, FSK, PSK, QPSK, QAM, PCM, etc.

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