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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
- a)2
- b)1
- c)e-1/2
- d)e
Correct answer is option 'B'. Can you explain this answer?
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The autocorrelation of a wide-sense stationary random process is given...
The autocorrelation of a wide-sense stationary random process is given by:
R(t1, t2) = E[X(t1)X(t2)]
where X(t) is the random process and E[.] denotes the expected value.
If we assume that the autocorrelation is given by e^(-2|t1-t2|), then the autocorrelation function is exponential in nature and decays exponentially with the time difference |t1-t2|. This implies that the random process has a memory that decays exponentially over time.
Note that the autocorrelation function can have different forms depending on the characteristics of the random process. The exponential form is just one example.
R(t1, t2) = E[X(t1)X(t2)]
where X(t) is the random process and E[.] denotes the expected value.
If we assume that the autocorrelation is given by e^(-2|t1-t2|), then the autocorrelation function is exponential in nature and decays exponentially with the time difference |t1-t2|. This implies that the random process has a memory that decays exponentially over time.
Note that the autocorrelation function can have different forms depending on the characteristics of the random process. The exponential form is just one example.
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The autocorrelation of a wide-sense stationary random process is given...
Concept:
The power spectral density is basically the Fourier transform of the autocorrelation function of the power signal, i.e.
Sx(f) = F.T.{Rx(τ)}
Analysis:
Given, the autocorrelation function of the random signal X(t) as:
RX(τ) = e−2|τ|
So, its power spectral density is obtained as:
D is at f = 0,SX(0) = 1
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