Programs and Documentation for Generating Gaussian White Noise and Colored Noise

In the field of signal processing, noise generation and simulation are common requirements, with Gaussian white noise and colored noise being the two most frequently used noise models.

Gaussian White Noise Gaussian white noise is a random signal with uniformly distributed power spectral density, characterized by equal energy across all frequency components and instantaneous values following a Gaussian distribution. In MATLAB implementation, the `randn` function generates Gaussian white noise sequences by producing standard normal distribution random numbers with zero mean and unit variance. To simulate noise with different characteristics, developers can scale the amplitude and adjust the mean value using mathematical operations like: noise_signal = mean + std_dev * randn(1,N), where N represents the sequence length and std_dev controls the variance.

Colored Noise Colored noise exhibits non-uniform power spectral density, typically demonstrating specific correlation or spectral characteristics. Common colored noise types include 1/f noise (pink noise) and ARMA (AutoRegressive Moving Average) model noise. MATLAB implementation involves filtering white noise using functions like `filter` with specific transfer functions. For example, colored noise can be generated by: colored_noise = filter(b, a, white_noise), where b and a represent the numerator and denominator coefficients of the filter respectively. Alternatively, developers can synthesize colored noise through random process modeling such as AR models using the `aryule` function for parameter estimation and `filter` for signal generation.

Program documentation typically includes noise parameter configuration (mean, variance, sampling rate), filter design methodologies (for colored noise generation), and visualization techniques for analyzing time-domain and frequency-domain characteristics using functions like `plot` for waveform display and `fft` for spectral analysis. Through these implementation steps, developers can flexibly generate Gaussian white noise and colored noise signals that meet practical application requirements while maintaining proper statistical properties and spectral characteristics.