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gaussian white noise process and autocorrelation

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meto

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gaussian white noise process

how to find autocorrelation Rv(τ)

v(t)=w(t)*cos(2Πft+Φ)

Φ and w(t) independent
w(t) gaussian white noise process

Thanks
 

my take:
Rvv = E{w(t1)*cos(2Πft1+Φ) * w(t2)*cos(2Πft2+Φ)}

since w and Φ are indep,
Rvv = E{w(t1) * w(t2)} * E{cos(2Πft1+Φ) * cos(2Πft2+Φ)}

first term =1 , assuming w has unit power
Rvv = E{cos(2Πf ((t1+t2) + 2Φ) * cos(2Πf(t1-t2))} * 1/2

first term evaluates to zero, assuming Φ is uniformily didstibuted between 0 and 2Π, second terms is deterministic.

Rvv(ζ) = cos(2Πfζ) * 1/2
-b

Added after 7 minutes:

but since w is given as white,

E{w(t1) * w(t2)} = 1 only when t1 = t2 and 0 else.

So then,
Rvv = 1/2

comments?
-b
 

    M

    meto

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