Signal Modulation and Demodulation Techniques in MATLAB: A Deep Dive

# 1. Fundamental Concepts of Signal Modulation and Demodulation

## 1.1 The Necessity of Signal Modulation and Demodulation
In modern communication systems, the transmission of information needs to span various distances and face complex transmission environments. Modulation and demodulation technology plays a crucial role in this process, capable of modulating baseband signals to higher frequencies, adapting to wireless or wired transmission, and demodulating at the receiving end to restore the original signal. Signal modulation and demodulation not only improve the transmission efficiency of signals but also enhance the抗干扰 ability of communication systems.

## 1.2 Basic Principles of Modulation and Demodulation
Modulation is a process of loading information signals onto a transmission medium, while demodulation is a process of extracting original information from the modulated signals. Modulation techniques include amplitude modulation (AM), frequency modulation (FM), and phase modulation (PM), among others. These modulation techniques are based on changing certain parameters of the carrier (such as amplitude, frequency, phase) to match the characteristics of the signal and transmission requirements.

## 1.3 Classification and Application Scenarios of Modulation and Demodulation
Depending on the type of transmission signal (analog or digital) and different modulation methods, modulation and demodulation technology can be classified into various categories, such as ASK, FSK, PSK, etc. These technologies are widely used in fields such as wireless communication, data communication, and satellite communication. Understanding the classification and application scenarios of these technologies is the basis for an in-depth exploration of modulation and demodulation.

Through the introduction of this chapter, we can establish a preliminary understanding of signal modulation and demodulation technology, laying a solid foundation for specific implementation and performance evaluation through MATLAB in subsequent chapters.

# 2. Signal Modulation Technology in MATLAB

### 2.1 Basic Theories of Modulation

#### 2.1.1 Definition and Classification of Modulation
Modulation is a technique that involves changing certain characteristics of the carrier signal (such as amplitude, frequency, or phase) to carry information signals. The process of modulation is the core of communication technology, allowing original signals (such as audio, video, or digital data) to be transmitted efficiently over different media. In the modulation process, the information signal is called the baseband signal, and the modulated signal is called the bandpass signal.

Modulation can be classified based on different standards. Depending on the type of modulation signal, it can be divided into analog modulation and digital modulation. Analog modulation is the modulation of analog baseband signals onto the carrier, while digital modulation is the modulation of digital baseband signals onto the carrier. Depending on the modulation parameters, it can be divided into amplitude modulation (AM), frequency modulation (FM), and phase modulation (PM).

#### 2.1.2 Basic Parameters and Characteristics of Modulation
The modulation process involves a series of key parameters, among which the most important are the carrier frequency, modulation index, bandwidth requirements, and signal-to-noise ratio (SNR). The carrier frequency determines the central frequency of signal transmission, while the modulation index describes the extent of the modulation signal's effect on the carrier. Bandwidth requirements refer to the frequency spectrum width required for signal transmission, which is closely related to the modulation method and modulation index. SNR is the ratio of signal strength to noise strength, directly affecting the quality and effectiveness of communication.

### 2.2 Signal Modulation Implementation in MATLAB

#### 2.2.1 Implementation of Analog Signal Modulation
In MATLAB, analog signal modulation can be implemented through built-in functions or programming. Taking amplitude modulation (AM) as an example, its basic form can be represented as:

\[ s(t) = [A_c + m(t)] \cdot \cos(2\pi f_c t + \phi) \]

where \( A_c \) is the carrier amplitude, \( m(t) \) is the modulation signal, \( f_c \) is the carrier frequency, and \( \phi \) is the carrier phase.

MATLAB code example:

Ac = 1; % Carrier amplitude
fc = 100; % Carrier frequency
t = 0:1/1000:1; % Time vector
m = cos(2*pi*10*t); % Modulation signal (sine wave at 10Hz)

% Amplitude modulation
AM_signal = (Ac + m) .* cos(2*pi*fc*t);

#### 2.2.2 Implementation of Digital Signal Modulation
The modulation of digital signals usually involves processing the digital baseband signal for transmission in communication systems. Taking Binary Phase Shift Keying (BPSK) as an example, it can be represented by the following formula:

\[ s(t) = \sqrt{\frac{2E_b}{T_b}} \cdot \cos(2\pi f_c t + \pi \cdot b_n) \]

where \( E_b \) is the energy per bit, \( T_b \) is the bit duration, \( b_n \) is the value of the \( n \)th bit (-1 or 1), and \( f_c \) is the carrier frequency.

MATLAB code example:

Eb = 1; % Energy per bit
Tb = 1; % Bit duration
data = [1 -1 1 1 -1 -1 1]; % Binary data
fc = 100; % Carrier frequency
t = 0:1/(1000*fc):length(data)*Tb; % Time vector

% BPSK modulation
BPSK_signal = sqrt(2*Eb/Tb) * cos(2*pi*fc*t + pi*(data-1)/2);

#### 2.2.3 Visual Presentation of Modulation Effects
Visualizing the modulated signal helps to understand the modulation effects and the modulation process. In MATLAB, functions such as `plot`, `spectrogram` can be used to display the time domain and frequency domain of the modulated signal.

figure;
subplot(2,1,1);
plot(t, AM_signal);
title('AM Signal');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(2,1,2);
plot(t, BPSK_signal);
title('BPSK Signal');
xlabel('Time (s)');
ylabel('Amplitude');

figure;
subplot(2,1,1);
spectrogram(AM_signal, 256, 250, 256, fc);
title('Spectrogram of AM Signal');

subplot(2,1,2);
spectrogram(BPSK_signal, 256, 250, 256, fc);
title('Spectrogram of BPSK Signal');

### 2.3 Performance Evaluation of Modulation Technologies

#### 2.3.1 Concepts of SNR and BER
Signal-to-Noise Ratio (SNR) is the ratio of signal power to background noise power, an important parameter for measuring the performance of a communication system. Bit Error Rate (BER) refers to the ratio of the number of bits transmitted incorrectly to the total number of bits transmitted, which is an indicator for evaluating the performance of a digital communication system.

#### 2.3.2 Performance Evaluation Methods and MATLAB Toolbox Application
In MATLAB, functions in the communication toolbox can be used to calculate SNR and BER. For instance, the `snr` function can be used to calculate signal-to-noise ratio, and the `bertool` can be used to analyze bit error rate performance.

% Calculate SNR
snr_val = snr(AM_signal, noise_signal); % noise_signal is additive Gaussian white noise

% Calculate BER
% Assuming BPSK_signal is the received signal and data is the original data
[~, ~, ~, ~, ber] = biterr(data, BPSK_signal > 0);

% Use BER Toolbox to evaluate performance
berTool;

Through the introduction of the above chapters, we understand the basic theories of signal modulation in MATLAB, as well as how to implement the modulation of analog and digital signals in the MATLAB environment. Additionally, by calculating performance evaluation indicators, we can more deeply understand the performance of modulation technologies in practical applications.

# 3. Signal Demodulation Technology in MATLAB

## 3.1 Basic Theories of Demodulation

### 3.1.1 Definition and Classification of Demodulation
Demodulation refers to the process of extracting original information from a modulated signal. In