# Creating White Noise with a Specific Standard Deviation in MATLAB

Jan 23, 2024

In the world of digital signal processing, white noise is a useful concept that can serve as an input signal to test and validate various algorithms. In essence, white noise represents a random signal with equal intensity at different frequencies. One important consideration when generating white noise is to control its standard deviation, which is a measure of the signal's intensity or variability. In this article, we will discuss how to generate white noise with a certain standard deviation (SD) in MATLAB.

First, let's generate white noise using the 'randn' function in MATLAB, which creates an array of random numbers following a standard normal distribution (mean = 0, SD = 1). You can create an Nx1 white noise column vector as follows:

```
N = 1000; % Length of the white noise vector
white_noise = randn(N, 1);
```

Now, having obtained the original white noise vector, we can control its standard deviation by multiplying the signal by the desired standard deviation value. Here's how to do it:

```
desired_sd = 5; % Specify the desired standard deviation
scaled_noise = desired_sd * white_noise;
```

That's it! You now have a white noise vector with a specific standard deviation. You can use it for various applications like testing the robustness of your algorithms or simulating various systems' response to random input signals.

If you wish to visualize your generated white noise, you can plot it using MATLAB's 'plot' function:

```
time = linspace(0, 10, N); % create a time vector
figure;
plot(time, scaled_noise);
xlabel('Time');
ylabel('Amplitude');
title('White Noise with a Specific Standard Deviation');
```

This will give you a time-domain representation of your white noise signal, helping you better understand how it behaves with the specified standard deviation.

In conclusion, generating white noise with a certain standard deviation in MATLAB is a straightforward process. By using the 'randn' function to create a white noise signal and then scaling it with the desired standard deviation, you can control the signal's intensity and variability. This makes it useful for a wide range of applications, from testing algorithms to simulating system responses.