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A Comprehensive Study with MATLAB Simulations

ANALOG AM AND FM MODULATIONS USING MATLAB

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INTRODUCTION

IMPORTANCE AND APPLICATIONS

Used in radio, TV broadcasting, and communication systems.

OBJECTIVES

Implement and analyze AM and FM using MATLAB.

01

02

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AMPLITUDE MODULATION (AM) THEORY

    • Modulation Index:
    • πœ‡=π΄π‘šπ΄π‘ΞΌ=Ac​Am​​

Definition: AM varies the amplitude of the carrier signal based on the message signal.

Mathematical Expression:

𝑠(𝑑)=[1+π‘š(𝑑)]β‹…cos⁑(2πœ‹π‘“π‘π‘‘)s(t)=[1+m(t)]β‹…cos(2Ο€fc​t)

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AM SIGNAL GENERATION IN MATLAB

% AM Modulated signal

s = (1 + m) .* c;

Message Signal (Example):

% Parameters

fc = 1000; % Carrier frequency

fs = 10000; % Sampling frequency

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

Am = 1; % Amplitude of message signal

Ac = 1; % Amplitude of carrier signal

fm = 100; % Frequency of message signal

​

% Message signal

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

AM Modulated Signal:

% Carrier signal

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

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AM SIGNAL VISUALIZATION

​

MATLAB Code for Plotting:

figure;

subplot(3,1,1);

plot(t, m);

title('Message Signal');

xlabel('Time (s)');

ylabel('Amplitude');

​

subplot(3,1,2);

plot(t, c);

title('Carrier Signal');

xlabel('Time (s)');

ylabel('Amplitude');

​

subplot(3,1,3);

plot(t, s);

title('AM Modulated Signal');

xlabel('Time (s)');

ylabel('Amplitude');

​

    • Plots:
      • Message Signal
      • Carrier Signal
      • AM Modulated Signal

​

​

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AM DEMODULATION

DEMODULATION TECHNIQUES:

MATLAB CODE FOR DEMODULATION:% ENVELOPE DETECTION

DEMODULATED_SIGNAL = ABS(HILBERT(S));

FIGURE;

PLOT(T, DEMODULATED_SIGNAL);

TITLE('DEMODULATED SIGNAL');

XLABEL('TIME (S)');

YLABEL('AMPLITUDE');

      • ENVELOPE DETECTION
      • SYNCHRONOUS DEMODULATION

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    • Definition: FM varies the frequency of the carrier signal based on the message signal.
    • Mathematical Expression:
    • 𝑠(𝑑)=𝐴𝑐cos⁑(2πœ‹π‘“π‘π‘‘+𝛽sin⁑(2πœ‹π‘“π‘šπ‘‘))s(t)=Ac​cos(2Ο€fc​t+Ξ²sin(2Ο€fm​t))
    • Modulation Index:
    • 𝛽=Ξ”π‘“π‘“π‘šΞ²=fm​Δf​

FREQUENCY MODULATION (FM) THEORY

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matlab

% Parameters

fc = 1000; % Carrier frequency

fs = 10000; % Sampling frequency

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

Am = 1; % Amplitude of message signal

Ac = 1; % Amplitude of carrier signal

fm = 100; % Frequency of message signal

beta = 5; % Modulation index

​

% Message signal

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

FM SIGNAL GENERATION IN MATLAB

MESSAGE SIGNAL (EXAMPLE):

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FM SIGNAL VISUALIZATION

MATLAB CODE FOR PLOTTING:

matlab

​

figure;

subplot(2,1,1);

plot(t, m);

title('Message Signal');

xlabel('Time (s)');

ylabel('Amplitude');

​

subplot(2,1,2);

plot(t, s);

title('FM Modulated Signal');

xlabel('Time (s)');

ylabel('Amplitude');

​

    • Plots:
      • Message Signal
      • FM Modulated Signal

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% FM Demodulation example using differentiation

demodulated_signal = diff(unwrap(angle(hilbert(s))));

figure;

plot(t(1:end-1), demodulated_signal);

title('Demodulated Signal');

xlabel('Time (s)');

ylabel('Amplitude');

Demodulation Techniques:

      • Zero-Crossing Detector
      • Phase-Locked Loop (PLL)
    • MATLAB Code for Demodulation:
    • matlab

FM DEMODULATION

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COMPARATIVE ANALYSIS OF AM AND FM

      • AM: 2𝐡2B
      • FM: β‰ˆ2(Δ𝑓+𝐡)β‰ˆ2(Ξ”f+B)

Bandwidth Requirements:

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      • AM is more susceptible to noise.
      • FM offers better noise immunity.

Noise Immunity:

      • AM: Used in AM radio.
      • FM: Used in FM radio, TV audio, and two-way radios.

Applications:

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      • AM and FM modulation techniques have distinct advantages and disadvantages.
      • MATLAB provides a powerful tool for simulating and analyzing these modulation techniques.
      • Explore other modulation techniques.
      • Real-time signal processing with hardware.

SUMMARY OF FINDINGS:

FUTURE WORK:

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