# Adding Random White Noise in MATLAB: A Step-by-Step Guide

Jan 23, 2024

When working with data or signals in MATLAB, simulating random white noise can help in analyzing the system's performance under various conditions. White noise is a random signal characterized by a constant power spectral density, meaning that its power is uniformly spread over a broad range of frequencies. In this article, we'll guide you through the process of adding random white noise to your data using MATLAB.

Generate or import your data: First, you need to have some data or a signal to which you want to add the white noise. You can either generate this data using MATLAB functions, or import it from external sources like .csv, .txt, or .wav files.

Determine the signal's power: Before adding white noise, you must determine the power of your original signal. This can be calculated using MATLAB's 'mean' and 'std' functions, as shown below:

```
signal_power = mean(abs(signal).^2);
```

Determine the desired noise-to-signal ratio (NSR): The NSR is a measure of the level of noise relative to your signal. It can be set at any value depending on your needs. For example, if you want the noise to be equally powerful as the signal, you can set NSR to 1. If you want the noise to be less powerful, you can set it to a lower value, like 0.5 or 0.1.

Generate random white noise: Use MATLAB's 'randn' function to generate white noise with the same length as your signal. The function creates a normally distributed random signal with a mean value of 0 and a standard deviation of 1. Multiply the noise by the desired standard deviation to match the required power of the noise:

```
noise = sqrt(signal_power * NSR) * randn(size(signal));
```

- Add the white noise to your signal: Now that you have generated the random white noise, simply add it to your original signal:

```
noisy_signal = signal + noise;
```

- Analyze and visualize the results: You can now visualize and analyze your new signal with added random white noise. Use MATLAB's built-in functions like 'plot', 'spectrogram', or 'pwelch' to display the time-domain waveform, spectrogram, or power spectral density of your noisy signal.

In conclusion, adding random white noise to a signal in MATLAB is a straightforward process. Following the steps outlined above, researchers and engineers can assess how their data or systems perform under various simulated noisy conditions. This is especially valuable when analyzing real-world data or testing the robustness of algorithms and signal processing techniques.