Capability to Generate Gaussian White Noise

In MATLAB simulation experiments, noise generation is a common requirement in fields such as signal processing and communication system testing. Gaussian white noise, as an idealized noise model, features a uniformly distributed power spectral density and amplitude following a Gaussian distribution. MATLAB provides multiple functions to generate this type of noise; for example, the `randn` function directly produces random sequences that follow a standard normal distribution. By adjusting the mean and variance parameters, one can simulate Gaussian white noise encountered in practical scenarios. Compared to white noise, colored noise exhibits a non-flat power spectral density with specific frequency distribution characteristics. Generating colored noise typically requires filtering white noise. Using MATLAB's filter design tools (such as the `filter` function or the `dsp.ColoredNoise` object), it is convenient to synthesize various colored noises like pink noise (1/f noise) and brown noise (1/f² noise). For more general noise types (such as impulse noise or periodic noise), they can be implemented by combining basic noise models or custom probability distributions. For instance, using random number generation functions (like `rand` or `randn`) combined with logical conditions can simulate burst impulse interference. By superimposing sine waves with noise, one can construct mixed noise containing periodic disturbances. In simulation experiments, validating the time-domain and frequency-domain characteristics of noise is crucial. MATLAB's `periodogram` or `pwelch` functions can be used to analyze the noise power spectrum, while statistical functions such as `mean`, `var`, and `histogram` help verify whether the amplitude distribution meets expectations. This workflow provides a flexible and reliable noise environment for research on communication system noise immunity testing and filter design.