MATLAB Code Implementation for Generating Gaussian White Noise with Signal Analysis

In this article, we demonstrate how to generate Gaussian white noise using MATLAB and visualize its time-domain waveform, autocorrelation function, and power spectrum density. Gaussian white noise is characterized as a random signal with zero mean, constant variance, and time-independent properties, making it particularly valuable in signal processing applications such as channel capacity testing in communication systems. The implementation begins with the randn function, which generates normally distributed random numbers with specified parameters. For instance, to create a Gaussian white noise sequence of length N with zero mean and unit variance, we use: noise = randn(1,N). The generated signal can then be visualized in the time domain using the plot function with proper axis labeling and scaling. For autocorrelation analysis, the xcorr function calculates the correlation of the signal with itself at different time lags. The unbiased autocorrelation can be obtained using xcorr(noise,'unbiased'), revealing the noise's statistical properties. The resulting function is plotted to show the characteristic impulse-like shape at zero lag, confirming the white noise characteristics. Power spectral density estimation is performed using the pwelch function, which implements Welch's method for spectral analysis. The command [pxx,f] = pwelch(noise,[],[],[],fs) returns the power spectrum estimate pxx at frequencies f, where fs represents the sampling frequency. The flat spectrum plot demonstrates the uniform power distribution across frequencies, a key feature of white noise. We further discuss how these analytical techniques validate the noise properties and their practical applications in system testing and simulation.