【Practical Exercise】Communication Principles MATLAB Simulation: Partial Response System

# 1. Fundamental Principles of Communication

Communication principles are the science of how information is transmitted. It encompasses the generation, modulation, transmission, reception, and demodulation of signals.

**Signal** is the physical quantity that carries information, which can be either analog or digital. Analog signals are continuously varying, while digital signals are discretely varying.

**Modulation** is the process of superimposing the information signal onto a carrier signal. The carrier signal is a signal with a frequency and amplitude higher than the information signal. Modulation can be amplitude modulation, frequency modulation, or phase modulation.

**Transmission** is the process of transmitting the modulated signal through a channel to the receiver. The channel can be wireless or wired.

**Reception** is the process of receiving the modulated signal and demodulating the information signal. Demodulation can be amplitude demodulation, frequency demodulation, or phase demodulation.

# 2. MATLAB Simulation Environment

MATLAB (Matrix Laboratory) is an advanced programming language and interactive environment widely used for technical computing, signal processing, and data analysis. It offers a rich collection of tools and libraries, enabling engineers and researchers to efficiently simulate and analyze partial response systems.

### 2.1 Basic Operations in MATLAB

**Variables and Data Types**

MATLAB uses variables to store data. Variable names start with a letter, followed by letters, numbers, or underscores. Data types include:

- Numeric: integers (int), floating-point numbers (double), and complex numbers (complex)
- Strings: text enclosed in single or double quotes
- Logical values: true or false
- Matrices: two-dimensional or multidimensional arrays
- Cell arrays: arrays containing different types of data

**Operators and Expressions**

MATLAB supports various operators, including arithmetic, logical, and relational operators. Expressions are used to perform calculations and produce results.

**Functions**

MATLAB provides a large number of built-in functions for mathematical computation, signal processing, and data analysis. Users can also create their own functions to extend the capabilities of MATLAB.

### 2.2 Signal Processing Toolbox

The MATLAB Signal Processing Toolbox is an extension module that provides specialized functions and tools for signal processing. It includes functions for:

- Signal generation and analysis
- Filter design and implementation
- Spectral estimation and power spectral density computation
- Image and video processing

**Signal Generation**

The Signal Processing Toolbox provides functions for generating various types of signals, such as:

- Sine wave: `sin()`
- Square wave: `square()`
- Sawtooth wave: `sawtooth()`
- Noise: `randn()` and `rand()`

**Filter Design**

The Signal Processing Toolbox provides functions for designing and implementing various filters, such as:

- FIR filters: `fir1()` and `fir2()`
- IIR filters: `butter()`, `cheby1()`, `cheby2()`
- Multirate filters: `multirate()`

**Spectral Estimation**

The Signal Processing Toolbox provides functions for estimating the power spectral density of signals, such as:

- Periodogram: `periodogram()`
- Welch method: `pwelch()`
- Multiple signal classification (MUSIC): `music()`

**Code Example**

% Generate a sine wave
t = 0:0.01:10;
y = sin(2*pi*10*t);

% Plot the signal
plot(t, y);
xlabel('Time (s)');
ylabel('Amplitude');
title('Sine Wave');

**Code Logic Analysis**

* Create a time vector `t`, with a step size of 0.01.
* Use the `sin()` function to generate a sine wave `y`, with a frequency of 10Hz.
* Use the `plot()` function to plot the signal.
* Add axis labels and a title.

# 3. Partial Response System Theory

### 3.1 Concepts and Classification of Partial Response Systems

**Concept:**

A partial response system (PRS) is a linear time-invariant (LTI) ***pared to a full response system (FRS), PRS has unique characteristics in both the frequency domain and the time domain.

**Classification:**

Based on the shape