Gaussian white noise is a crucial concept in signal processing and controls systems, often used for simulation and analysis purposes in MATLAB/Simulink. Its application can be seen in various domains such as testing control systems, modeling real-world phenomena, and adding randomness in algorithms. Here is a guide on how to apply Gaussian white noise in MATLAB and Simulink:

In MATLAB

1. Using randn Function:

   The randn function in MATLAB generates samples from a standard normal distribution (mean = 0, variance = 1). To create Gaussian white noise with a specific variance, you can scale the output of randn.

   % Parameters  
   n = 1000; % Number of samples  
   variance = 0.5;  
   % Generate Gaussian white noise  
   noise = sqrt(variance) * randn(n, 1);  
   % Plot the noise  
   figure;  
   plot(noise);  
   title('Gaussian White Noise');  
   xlabel('Sample Index');  
   ylabel('Amplitude');  

2. Simulating Noisy Signals:

   You can add Gaussian white noise to existing signals to simulate real-world measurement noise.

   % Original Signal  
   t = linspace(0, 1, n);  
   signal = sin(2 * pi * 5 * t);  
   % Add Gaussian White Noise  
   noisy_signal = signal + noise';  
   % Plot the original and noisy signals  
   figure;  
   plot(t, signal, 'b', t, noisy_signal, 'r');  
   legend('Original Signal', 'Noisy Signal');  
   title('Signal with Gaussian White Noise');  
   xlabel('Time (s)');  
   ylabel('Amplitude');  

In Simulink

1. Using the Random Number Block:

   Simulink provides a convenient way to introduce white noise into your models using the "Random Number" block. Here’s how you can set it up:

• Open your Simulink model.
• Drag and drop the "Random Number" block from the Simulink Library Browser (under the "Sources" category).
• Double-click on the block to configure its parameters:
  • Mean: Set it to 0 for zero-mean Gaussian noise.
  • Variance: Set this to your desired noise variance.
  • Seed: Set an initial seed for reproducibility.

2. Adding Noise to a Signal:

• Connect the "Random Number" block to an input of an "Add" block or directly add it to the signal lines you wish to introduce noise.
• Ensure the sample time of the "Random Number" block matches your system's requirements or the sample time of the other signals in your model.

3. Running the Simulation:

• Configure the simulation parameters like stop time and solver options.
• Run the simulation to see how the noise affects your system or signal.

Practical Considerations

• Noise Characteristics: Ensure the noise's statistical properties (mean and variance) match your specific application needs.
• Reproducibility: Setting the seed for random number generation ensures that simulations are repeatable across runs, which can be crucial for testing and debugging.
• Filtering and Analysis: After introducing noise, you may want to analyze its effect on your system. Techniques such as filtering (e.g., via Kalman filters) or spectral analysis are common follow-up steps.

By understanding and using Gaussian white noise effectively, you can robustly test and improve your control systems, signal processing algorithms, and more within the MATLAB/Simulink environment.