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[SOLVED] autocorrelation definition

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SanjKrish

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Hello all,

I have been using this definition of autocorrelation very often
Rx(t) = E[x(t)x(t+T)]

but suddenly I got stumped to find my textbook using this definition
Rx(t) = Σx(t)x(t+T)



I could figure out expectation operation is nothing but averaging and so the first definition should lead to the second one,,, but in case if I am averaging N samples of x(n), where is the divided by N term or (1/N) in the second formula...
 

The first formula usually uses for random processes analysis. In this case operator E means average by realizations of random process.

The second formula usually uses for determinate signals analysis.
 
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