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Belyi shum
6.08.2001 0:00 | "Fizicheskaya Enciklopediya"/Phys.Web.Ru

Belyi shum - shum, vremya korrelyacii kotorogo mnogo men'she vseh harakternyh vremen fizicheskoi sistemy. Matematicheskoi model'yu belogo shuma sluzhit sluchainyi process $\xi(t)$ $(\lt\xi(t)\gt=0)$ s korrelyacionnoi funkciei
$$\Gamma(t,\tau)=\lt\xi(t+\tau)\xi(t)\gt=\sigma^2(t)\delta(\tau)$,$ (1)

gde $\delta(\tau)$ - del'ta-funkciya, $\le...\gt)$ - statisticheskoe usrednenie. $\sigma^2(t)$ - intensivnost' belogo shuma. V sluchae stacionarnogo processa $\sigma^2(t)=const$ , prichem korrelyacionnoi funkcii (1) otvechayut ravnomernyi spektr
$$\tilde{\Gamma}(\omega)=(2\pi)^{-1}\int_{-\infty}^{\infty}\Gamma(\tau) exp(-i\omega\tau)d\tau=\sigma^2/2\pi$,$ (2)

ravnoe nulyu vremya korrelyacii $\tau_k$ i v sootvetstvii s sootnosheniem neopredelennosti $\tau_k\Delta\omega\gt1$ beskonechnaya shirina spektra $\Delta\omega$ .
Model' belogo shuma ispol'zuyut dlya opisaniya vozdeistviya shumov s malym vremenem korrelyacii na fizicheskie sistemy (signaly), obladayushie konechnoi shirinoi polosy propuskaniya (spektra), v predelah kotoroi spektr real'nogo shuma mozhno schitat' priblizhenno ravnomernym. Primerom belogo shuma yavlyaetsya drobovoi shum, vremya korrelyacii kotorogo opredelyaetsya vremenem proleta elektrona ot katoda k anodu. Spektr drobovogo shuma ravnomeren do chastoty $\sim 10^8$ Gc. Drugoi primer - teplovoi shum, spektr kotorogo ravnomeren v tom intervale chastot, gde postoyanno soprotivlenie istochnika shuma. V oblasti slyshimyh chastot primerom belogo shuma yavlyaetsya shum vodopada.

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