【Basic】Signal Multiplexing and Demultiplexing in MATLAB: Implementing Frequency Division Multiplexing and Time Division Multiplexing

# 1. Overview of Signal Multiplexing and Demultiplexing

Signal multiplexing is a technique that combines multiple signals into a single physical channel for simultaneous transmission. Signal demultiplexing is the process of separating a multiplexed signal back into its original components. Multiplexing and demultiplexing are widely used in communication, data acquisition, and processing fields.

**Basic Principles:**

***Multiplexing:** Combining multiple signals into a composite signal, known as a multiplexed signal.
***Demultiplexing:** Extracting the original signals from a multiplexed signal.

**Multiplexing Techniques:**

***Frequency Division Multiplexing (FDM):** Allocating different frequency signals to different frequency bands and then combining them.
***Time Division Multiplexing (TDM):** Transmitting signals in different time periods, forming a sequence.

# 2. Signal Multiplexing in MATLAB

### 2.1 Frequency Division Multiplexing (FDM)

#### 2.1.1 Principles and Implementation of FDM

Frequency Division Multiplexing (FDM) is a multiplexing technique that modulates multiple signals onto different frequency carriers. Each signal occupies a specific frequency band, allowing for the simultaneous transmission of multiple signals on the same transmission medium.

#### 2.1.2 Example Implementation of FDM in MATLAB

% Carrier frequencies
fc1 = 1000;
fc2 = 2000;

% Modulating signals
m1 = sin(2*pi*100*t);
m2 = sin(2*pi*200*t);

% Modulating carriers
c1 = cos(2*pi*fc1*t);
c2 = cos(2*pi*fc2*t);

% FDM signal
fdm_signal = m1 .* c1 + m2 .* c2;

### 2.2 Time Division Multiplexing (TDM)

#### 2.2.1 Principles and Implementation of TDM

Time Division Multiplexing (TDM) is a multiplexing technique that alternates the transmission of multiple signals on the same transmission medium. Each signal occupies a specific time slot, allowing for the simultaneous transmission of multiple signals on the same transmission medium.

#### 2.2.2 Example Implementation of TDM in MATLAB

% Sampling frequency
fs = 1000;

% Signals
s1 = sin(2*pi*100*t);
s2 = sin(2*pi*200*t);

% TDM signal
tdm_signal = [s1(1:fs/2), s2(1:fs/2)];

### 2.3 Applications of Signal Multiplexing and Demultiplexing in MATLAB

#### 2.3.1 Applications of FDM and TDM in Communication Systems

FDM and TDM are widely used in communication systems, for example:

- **FDM:** Used for amplitude modulation broadcasting and television broadcasting.
- **TDM:** Used for telephone systems and digital communication systems.

#### 2.3.2 Applications of FDM and TDM in Data Acquisition

FDM and TDM can also be used in data acquisition, for example:

- **FDM:** Used for acquiring data from different sensors.
- **TDM:** Used for acquiring data from the same sensor at different time points.

# 3. Signal Demultiplexing in MATLAB

### 3.1 Frequency Domain Demultiplexing (FDD)

#### 3.1.1 Principles and Implementation of FDD

Frequency Domain Demultiplexing (FDD) is a technique that achieves multiplexing by assigning signals to different frequency ranges. In FDD, each signal occupies a specific frequency band, and there are guard bands between these frequency bands to prevent interference.

In MATLAB, the `fft` and `ifft` functions can be used to implement FDD. The `fft` function performs a Fast Fourier Transform, converting time-domain signals into frequency-domain signals. The `ifft` function performs the inverse Fast Fourier Transform, converting frequency-domain signals back into time-domain signals.

#### 3.1.2 Example Implementation of FDD in MATLAB

% Signal generation
fs = 1000; % Sampling rate
t = 0:1/fs:1; % Time vector
f1 = 100; % Signal 1 frequency
f2 = 200; % Signal 2 frequency
x1 = sin(2*pi*f1*t); % Signal 1
x2 = sin(2*pi*f2*t); % Signal 2

% Frequency Division Multiplexing
X = fft(x1 + x2); % Perform FFT
N = length(X); % Signal length
f = (0:N-1)*(fs/N); % Frequency vector

% Extract Signal 1 and Signal 2
bandwidth = 50; % Guard band width
f1_start = f1 - bandwidth/2;
f1_end = f1 + bandwidth/2;
f2_start = f2 - bandwidth/2;
f2_end = f2 +