13.16. Consider the network shown in Fig. P13.16, where is a random voltage with zero mean and autocorrelation function .

Find the power spectrum . What is the transfer function? Find the power spectrum .

x(t) = x1(t) – 2x1(t – 5) + x1(t – 10)

Rx1

(t) Rx(t) x1(t) t2 = exp(– ⁄ 2)

Ry(t)

y(t) YnRect t – n5 2

-------------  

 

n = 1 5

= Σ

Yn { } = {0.8, 1, 1, 1, 0.8}

Sy (ω)

h(t)

exp(–2t) t ≥ 0

0 t < 0 

 

 

=

Rh (τ)

x(t) = 3cos(100t)

vdc n(t) σn 2

x(t) = vdc + n(t) vdc x(t)

vdc ≈ (x1 + x2 + x3) ⁄ 3

)

vdc

)

vdc x(t)

ℜx (τ) = 1 + exp(–a t )

Sx (ω)

Sv (ω)