The autocorrelation function RX (τ) of a wide-sense stationary random process X (t) is shown in the figure,The average power of X (t) is ______.Correct answer is '2'. Can you explain this answer?

Question

The autocorrelation function RX (&tau;) of a wide-sense stationary random process X (t) is shown in the figure,The average power of X (t) is ______.Correct answer is '2'. Can you explain this answer?

Answer

Method 1

Given, autocorrelation function R_X (τ) of wide sense stationary random process X (t) is shown in figure.

Here, R_X(τ=0)=2

Method 2 :

From standard result,

Energy of sinc ( f ) = 1

Using scaling property,

Energy of sinc (2 f ) = 1 /2

From equation (iii),

Hence, average power of X (t) is 2 W.

Question_Type: 4

Answer

Method 1

Given, autocorrelation function R_X (τ) of wide sense stationary random process X (t) is shown in figure.

Here, R_X(τ=0)=2

Method 2 :

From standard result,

Energy of sinc ( f ) = 1

Using scaling property,

Energy of sinc (2 f ) = 1 /2

From equation (iii),

Hence, average power of X (t) is 2 W.

Question_Type: 4

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