White noise

White noise is a random signal with equal power per unit frequency across a specified bandwidth. When heard, it sounds like a steady broadband hiss.

Power spectral density: A function describing how a signal’s power is distributed over frequency. White noise is defined by constant power spectral density across its specified bandwidth.
Random process: A collection of random variables indexed by time, space, or another parameter. White noise is modeled as a random process rather than a predictable waveform.
Pink noise: Noise whose power spectral density decreases inversely with frequency. Unlike white noise, pink noise allocates equal power to each octave.
System identification: The process of inferring a system’s behavior from observed inputs and outputs. Broadband excitation can reveal a system’s response across many frequencies at once.
Autocorrelation: A measure of how strongly a signal resembles a time-shifted version of itself. Ideal white noise has zero autocorrelation at every nonzero time lag.
Stationary process: A stochastic process whose statistical properties do not change under time shifts. Stationarity provides a framework for describing white noise with stable statistics.
Brownian noise: Noise whose power spectral density decreases approximately as the inverse square of frequency. Its strong low-frequency emphasis contrasts with white noise’s flat spectrum.
Convolution: A mathematical operation combining two functions to describe filtering and linear system responses. Passing white noise through a system produces an output shaped by its impulse response.
Bandwidth: The range of frequencies occupied or transmitted by a signal. Real white noise is flat only within a finite frequency range.
Gaussian distribution: A symmetric probability distribution shaped like a bell curve and specified by its mean and variance. Gaussian white noise uses this distribution for its instantaneous amplitudes.

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