RandomNoise

Random noise refers to a signal containing seemingly unpredictable, irregular fluctuations in amplitude over time or space. It is used as a simple model of uncontrollable variability in physical systems and as a tool in analysis and simulation. Random noise encompasses a range of statistical processes with different spectral and distributional properties.

A common distinction is by spectral content. White noise has a flat power spectral density, meaning equal energy per unit bandwidth across frequencies. Pink noise (1/f) has more energy at lower frequencies, while brownian or red noise (1/f^2) emphasizes low frequencies even more. Other colors describe different spectral shapes, reflecting how energy is distributed across frequencies.

Generation methods include physical sources and software synthesis. Physical sources arise from intrinsic randomness in electronic components (thermal, shot, or avalanche noise). Software can generate noise by sampling uniform or Gaussian random numbers; formulas or filters can shape spectral content to produce colored noise. True randomness typically requires physical processes; pseudo-random number generators produce deterministic sequences that can mimic randomness for practical purposes.

Key properties include stationarity, mean, variance, and correlations. White noise is often modeled as an independent, identically distributed sequence with zero or fixed mean and finite variance; its autocorrelation is a delta function. Gaussian noise refers to amplitude values drawn from a normal distribution, while uniform noise uses a flat distribution within a range.

Applications span testing and calibration of systems, channel simulations in communications, dithering in digital audio and imaging, masking effects in psychoacoustics, and various Monte Carlo or stochastic modeling tasks. Measurement relies on analyzing the power spectral density and autocorrelation to characterize whiteness and color.