[Practical Exercise] FM Modulation and Demodulation Implementation in MATLAB

# 1. Basic Knowledge of MATLAB**

MATLAB (Matrix Laboratory) is a high-level programming language extensively used for technical computing. It boasts powerful numerical analysis, data visualization, and algorithm development capabilities. MATLAB is widely applied across various fields including engineering, science, finance, and machine learning.

The fundamental data structure in MATLAB is the matrix, making it particularly suitable for handling large datasets and performing linear algebra operations. MATLAB also offers a rich library of functions, spanning tasks from signal processing to image processing. Its interactive environment and easy-to-use syntax make it an ideal choice for both beginners and experienced developers.

# 2. Modulation Theory and MATLAB Implementation

### 2.1 Basics of Modulation Theory

#### 2.1.1 Concept and Classification of Modulation

Modulation is a process of superimposing an information signal (baseband signal) onto a carrier signal to facilitate information transmission. Modulation is divided into two types:

- **Analog Modulation:** The information signal is a continuous analog signal, and the carrier signal is also a continuous analog signal.
- **Digital Modulation:** The information signal is a discrete digital signal, and the carrier signal is a continuous analog signal or a discrete digital signal.

#### 2.1.2 Principles and Formulas of FM Modulation

Frequency modulation (FM) is an analog modulation technique in which the frequency of the carrier signal varies with the amplitude of the information signal. The formula for FM modulation is as follows:

s(t) = A * cos(2πf_c * t + 2πk_f * m(t))

Where:

- `s(t)`: The modulated signal
- `A`: The amplitude of the carrier signal
- `f_c`: The frequency of the carrier signal
- `k_f`: The modulation index
- `m(t)`: The information signal

### 2.2 MATLAB Implementation of FM Modulation

#### 2.2.1 Implementation of the FM Modulation Function

The `fmdemod()` function in MATLAB can be used to implement FM modulation:

function modulatedSignal = fmModulate(carrierFreq, modFreq, modIndex, messageSignal)
% carrierFreq: Carrier frequency
% modFreq: Modulation frequency
% modIndex: Modulation index
% messageSignal: Information signal

% Calculate the modulated signal
modulatedSignal = fmdemod(messageSignal, carrierFreq, modFreq, modIndex);
end

#### 2.2.2 Setting Modulation Parameters and Signal Generation

The following code example demonstrates how to use the `fmModulate()` function to generate an FM modulated signal:

% Carrier frequency
carrierFreq = 1000; % Hz

% Modulation frequency
modFreq = 100; % Hz

% Modulation index
modIndex = 5;

% Information signal
messageSignal = sin(2 * pi * modFreq * t);

% Generate the modulated signal
modulatedSignal = fmModulate(carrierFreq, modFreq, mod