Amplitude, Frequency, and Phase Modulation Techniques

 

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');

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

[1] DSB and SSB-SC

 

2. Digital Modulation Techniques:

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