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Question: Prove the following two properties of the autocorrelation function R X (?) of a random…

Question: Prove the following two properties of the autocorrelation function R X (?) of a random…

Prove the following two properties of the autocorrelation function RX(?) of a random process X(t):

(a) If X(t) contains a DC component equal to A, then RX(?) will contain a constant component equal to A2.

(b) If X(t) contains a sinusoidal component, then RX(?) will also contain a sinusoidal component of the same frequency.

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Question:
Prove the following two properties of the autocorrelation function RX(?) of a random process X(t):
If X(t) contains a DC component equal to A, then RX(?) will contain a constant component equal to A2.
If X(t) contains a sinusoidal component, then RX(?) will also contain a sinusoidal component of the same frequency.

 

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