The autocorrelation of a wide-sense stationary random process

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The autocorrelation of a wide-sense stationary random process is given by e^{– 2|τ|} The peak value of the spectral density is—

1. 2
2. 1
3. e^{– 1/2}
4. e

Correct Option: B

Given that
R_xx(τ) = e^{– 2|t|}
then spectral density will be

S_xx(ω) =	2a	where, a = 2
	a² + ω²

Spectral density will be maximum at zero frequency
i.e., ω = 0

So, S_xx (0)_max =	2a		2 × 2	= 1
	a²		2²

Hence, alternative (B) is the correct choice.