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white noiseSee noise.
a generalized stochastic process of the type
where ϕ(t) is a finite function and X(t) is a stochastic process with zero mathematical expectation and with the correlation function B(s, t) = δ(s – t). The generalized function δ is determined by the formula
for any finite functions ϕk(t), where k = 1,2. This process is a stationary stochastic process with a spectral density f(λ) = ½π, –∞ <λ < ∞, and with an absolutely continuous spectral measure
F(Δ) = ʃΔf(λ)dλ
White noise is used as a mathematical model in theoretical studies. Noise of any nature that has a uniform spectrum in a finite band of frequencies, such as the noise of electronic tubes, atmospheric noise, and oceanic noise, can be approximated quite well by the white-noise process.