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The value of x(t) is expressed as a probability function.
* 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,
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<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
<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>
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