【Practical Exercise】Simulation of Analog Modulation Systems AM\DSB\SSB Based on MATLAB

# 2.1 Basic Principles of Modulation Theory

Modulation is the process of loading an information signal (baseband signal) onto a carrier signal (high-frequency signal) to enable long-distance transmission. The fundamentals of modulation theory mainly involve the following aspects:

- **Amplitude Modulation (AM):** AM maps the amplitude variations of the baseband signal onto the amplitude variations of the carrier signal.
- **Double Sideband Modulation (DSB):** DSB modulates both the positive and negative frequency components of the baseband signal onto the carrier signal, forming two sidebands.
- **Single Sideband Modulation (SSB):** SSB modulates either the positive or negative frequency components of the baseband signal onto the carrier signal, resulting in only one sideband and thus reducing spectral occupancy.

# 2. Principles of Analog Modulation Systems and Their MATLAB Implementation

### 2.1 Basic Principles of Modulation Theory

#### 2.1.1 Amplitude Modulation (AM)

Amplitude Modulation (AM) is a modulation technique that maps the amplitude variations of an analog signal (such as an audio signal) onto the amplitude variations of a carrier signal (such as an RF signal). The mathematical expression for AM modulation is:

y(t) = A_c(1 + m * x(t)) * cos(2πf_c t)

Where:

* `y(t)`: The modulated signal
* `A_c`: The amplitude of the carrier signal
* `m`: The modulation index, representing the ratio of the modulating signal amplitude to the carrier signal amplitude
* `x(t)`: The modulating signal
* `f_c`: The frequency of the carrier signal

#### 2.1.2 Double Sideband Modulation (DSB)

Double Sideband Modulation (DSB) is a modulation technique that shifts the spectrum of an analog signal to both sides of the carrier signal's spectrum. The mathematical expression for DSB modulation is:

y(t) = A_c * x(t) * cos(2πf_c t)

Where:

* `y(t)`: The modulated signal
* `A_c`: The amplitude of the carrier signal
* `x(t)`: The modulating signal
* `f_c`: The frequency of the carrier signal

#### 2.1.3 Single Sideband Modulation (SSB)

Single Sideband Modulation (SSB) is a modulation technique that shifts the spectrum of an analog signal to one side of the carrier signal's spectrum. The mathematical expression for SSB modulation is:

y(t) = A_c * x(t) * cos(2πf_c t + θ)

Where:

* `y(t)`: The modulated signal
* `A_c`: The amplitude of the carrier signal
* `x(t)`: The modulating signal
* `f_c`: The frequency of the carrier signal
* `θ`: The phase shift

### 2.2 MATLAB Signal Processing Toolbox

The MATLAB Signal Processing Toolbox provides a suite of functions for signal generation, processing, filtering, and modulation.

#### 2.2.1 Signal Generation and Processing Functions

* `sin`: Generate sine wave
* `cos`: Generate cosine wave
* `sawtooth`: Generate sawtooth wave
* `square`: Generate square wave
* `filter`: Filter signals
* `fft`: Perform Fourier transform on signals

#### 2.2.2 Filtering and Modulation Functions

* `ammod`: Amplitude modulate signals
* `dsbmod`: Double sideband modulate signals
* `ssbmod`: Single sideband modulate signals
* `amdemod`: Demodulate amplitude-modulated signals
* `dsbdemod`: Demodulate double sideband signals
* `ssbdemod`: Demodulate single sideband signals

# 3. AM Modulation System Simulation

### 3.1 AM Modulator Design

#### 3.1.1 Selection of Modulation Index and Carrier Frequency

The modulation index (m) is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier signal. It determines the extent to which the modulating signal affects the carrier signal. A higher modulation index means greater influence of the modulating signal on the carrier signal and more distortion in the output modulated signal waveform.

The selection of carrier frequency depends on the bandwidth of the modulating signal. The carrier frequency must be high enough to prevent overlap between the spectra of the modulating signal and the carrier signal. Generally, the carrier frequency sho