%% Analog Modulation Simulation

% This script demonstrates AM, FM, and PM modulation techniques with analysis

clear all;

close all;

clc;

%% Basic Parameters

fs = 10000; % Sampling frequency (Hz)

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

fc = 100; % Carrier frequency (Hz)

fm = 10; % Message signal frequency (Hz)

Ac = 1; % Carrier amplitude

Am = 0.5; % Message signal amplitude

%% Message and Carrier Signals

message_signal = Am*cos(2*pi*fm*t);

carrier_signal = Ac*cos(2*pi*fc*t);

%% 1. Amplitude Modulation (AM)

modulation_index = 0.7; % Modulation index (0 < m

design and simulate different types of analog modulation using MATLAB, you can follow these steps:

1. Understanding Analog Modulation Types

Analog modulation includes various techniques such as:

Amplitude Modulation (AM)

Frequency Modulation (FM)

Phase Modulation (PM)

Each of these modulations can be simulated in MATLAB using mathematical expressions and built-in functions.

2. Signal Generation

First, generate a message signal (modulating signal), which is usually a low-frequency sinusoidal signal:

fs = 10000; % Sampling frequency

t = 0:1/fs:0.1; % Time vector

fm = 50; % Message signal frequency

Am = 1; % Message amplitude

m = Am * sin(2 * pi * fm * t); % Message signal

3. Modulation Implementation in MATLAB

(a) Amplitude Modulation (AM)

fc = 1000; % Carrier frequency

Ac = 2; % Carrier amplitude

AM_signal = (1 + 0.5 * sin(2 * pi * fm * t)) .* (Ac * cos(2 * pi * fc * t));

figure;

subplot(3,1,1); plot(t, m); title('Message Signal');

subplot(3,1,2); plot(t, Ac * cos(2 * pi * fc * t)); title('Carrier Signal');

subplot(3,1,3); plot(t, AM_signal); title('Amplitude Modulated Signal');

(b) Frequency Modulation (FM)

kf = 100; % Frequency sensitivity factor

FM_signal = Ac * cos(2 * pi * fc * t + kf * sin(2 * pi * fm * t));

figure;

plot(t, FM_signal); title('Frequency Modulated Signal');

xlabel('Time (s)'); ylabel('Amplitude');

(c) Phase Modulation (PM)

kp = pi/2; % Phase sensitivity factor

PM_signal = Ac * cos(2 * pi * fc * t + kp * sin(2 * pi * fm * t));

figure;

plot(t, PM_signal); title('Phase Modulated Signal');

xlabel('Time (s)'); ylabel('Amplitude');

4. Spectrum Analysis Using FFT

To analyze the frequency spectrum of the modulated signals, use Fast Fourier Transform (FFT):

L = length(t);

Y = abs(fft(AM_signal, L)); % Compute FFT

f = fs*(0:(L/2))/L; % Frequency vector

figure;

plot(f, Y(1:L/2+1)); title('Spectrum of AM Signal');

xlabel('Frequency (Hz)'); ylabel('Magnitude');

5. MATLAB Simulink Approach (Alternative)

Instead of coding, you can use Simulink:

Open MATLAB, go to Simulink.

Create a model using Sine Wave (Message Signal), Carrier Signal, and Modulation Blocks.

Use Spectrum Analyzer for frequency analysis.