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* Auto-covariance function (ACF) <math>R_x(t,\tau)</math>
:<math>R_x(t,\tau) = E[x(t+\tau/2)x^*(t-\tau/2)]</math>
:In usual, we suppose that <math>E[x(t)] = 0 </math> for any t, :<math>E[x(t+\tau/2)x^*(t-\tau/2)]</math>
:<math>=\iint x(t+\tau/2,\xi_1)x^*(t-\tau/2,\xi_2)P(\xi_1,\xi_2)d\xi_1d\xi_2</math>
:(alternative definition of the auto-covariance function) :<math>\overset{\land}{R_x}(t,\tau)=E[x(t)x(t+\tau)]</math>
* Power spectral density (PSD) <math>S_x(t,f)</math>
:<math>S_x(t,f) = \int_{-\infty}^{\infty} R_x(t,\tau)e^{-j2\pi f\tau}d\tau</math>
* Relation between the [[Wigner distribution function|WDF (Wigner Distribution Function)]] and the PSD
:<math>E[W_x(t,f)] = \int_{-\infty}^{\infty} E[x(t+\tau/2)x^*(t-\tau/2)]\cdot e^{-j2\pi f\tau}\cdot d\tau</math>
:<math>= \int_{-\infty}^{\infty} R_x(t,\tau)\cdot e^{-j2\pi f\tau}\cdot d\tau</math><math>= S_x(t,f)</math>
* Relation between the [[ambiguity function]] and the ACF
:<math>E[A_X(\eta,\tau)] = \int_{-\infty}^{\infty} E[x(t+\tau/2)x^*(t-\tau/2)]e^{-j2\pi t\eta}dt</math>
:<math>= \int_{-\infty}^{\infty} R_x(t,\tau)e^{-j2\pi t\eta}dt</math>
=== Stationary random processes ===
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