The auto correlation function RX(τ) of a wide-sense stationary random process X(t) is shown in the figure.

The average power of X(t) is _______

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GATE EC 2021 Official Paper

Free

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

__Concept__**:**

Power spectral density of a wide sense stationary process is a positive real function.

It is related to Auto co-relation function Rx(τ) by:

\({R_x}\left( \tau \right)\begin{array}{*{20}{c}} {Fourier}\\ \leftrightarrow \\ {transform} \end{array}{S_x}\left( f \right)\)For wide – sense stationary random process, the power of a signal is given by R_{x}(0).

__Application__**:**

R_{x}(0) = 2

Average power of signal = R_{x}(0) = 2

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