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Correlated Signal with Noise - Question regarding to Expectation

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jeanpierre_33

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Hi All,

I would like to learn that,

r(t)=x(t) + n(t) , n is noise and x is desired signal

if x is uncorrelated then the Expectation(E)=[r(t) r(t+Δt)] =0

but if x is correlated then what should be the Expectation(E)=[r(t) r(t+Δt)] ?

also what is the difference between energy detector of correlated and uncorrelated signal when we have finite number of entries for example ∑(upper k-1) and(lower i=0) |r(t)|^2 and k<<∞ (for example k=10)?

Thanks in advance

JP
 
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