White Noise Testing in Random Signal Analysis Experiments

In random signal analysis experiments, we conduct white noise testing. White noise signals possess multiple characteristics including mean, variance, correlation function, probability density, frequency spectrum, and power spectral density. To analyze these properties programmatically, we typically implement functions that generate white noise using random number generators (e.g., randn() in MATLAB for Gaussian white noise), compute statistical measures through functions like mean() and var(), and estimate spectral characteristics using Fast Fourier Transform (FFT) algorithms and periodogram methods. The autocorrelation function can be calculated using xcorr() to verify the theoretical delta function property of ideal white noise. Through the investigation of these characteristics, we can better understand and analyze the properties of white noise signals. White noise testing serves as a fundamental experiment in the signal processing field, holding significant importance for studying the characteristics of random signals and noise. The experimental implementation typically involves comparing theoretical expectations with computed results to validate the whiteness property across different statistical measures.