Generation of Gaussian Random Signals and Gaussian White/Colored Noise with MATLAB Implementation

This documentation presents three comprehensive MATLAB code implementations. First, we generate Gaussian random signals, Gaussian white noise, and colored noise using MATLAB's built-in functions. Subsequently, we compute their numerical characteristics and perform spectral analysis and power spectrum analysis on these signals. Additionally, basic explanations regarding low-pass filter design are provided. Below, I elaborate on the implementation details for each section.

The first code segment generates Gaussian random signals using MATLAB's random number generation functions like randn() which produces normally distributed random numbers. These generated sequences simulate various system noises or signals in communication systems and signal processing applications, with parameters adjustable for different mean values and standard deviations.

The second implementation creates Gaussian white noise and colored noise. Gaussian white noise maintains constant power spectral density across frequencies, generated directly using randn(). For colored noise with non-uniform power spectral density, we apply filtering operations using MATLAB's filter() function or signal processing toolbox functions to modify the frequency characteristics of white noise, typically through autoregressive (AR) or moving average (MA) processes.

The third code segment performs spectral analysis and power spectrum analysis using MATLAB's Fast Fourier Transform (fft()) function for frequency component examination and Power Spectral Density (PSD) estimation functions like pwelch() or periodogram() for power distribution analysis. These analyses help characterize signal properties in both time and frequency domains.

Finally, basic low-pass filter design principles are explained using MATLAB's filter design functions such as fir1() for FIR filters or butter() for IIR filters. Low-pass filters attenuate high-frequency components while preserving low-frequency information, crucial for noise reduction and signal conditioning applications.

In summary, this implementation demonstrates complete MATLAB workflow for generating Gaussian random signals, white/colored noise, performing numerical characterization, spectral/power analysis, and introduces fundamental filter design concepts. These code examples provide practical foundation for signal processing applications and noise analysis studies.