Let r[n] be the random process that is generated by filtering white noise w[n] ~ N(0, 2) with a discrete-time filter that is designed by applying the bilinear transform to a continuous-time filter. The system function of the continuous-time filter is given as 2(s+ 1) H(s) 3s +1 For the sampling period Ta = 2, find the transfer function of the system H(2). a. b. Find the power spectrum Pw(2) of w[n] and Px(z) of r[n].

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Let r[n] be the random process that is generated by filtering white
noise w[n] ~ N(0, 2) with a discrete-time filter that is designed by applying the bilinear
transform to a continuous-time filter. The system function of the continuous-time filter is
given as
2(s+1)
3s +1
H(s) =
For the sampling period Ta = 2, find the transfer function of the system H(2).
а.
%3D
b.
Find the power spectrum Pw(z) of w[n] and Px(z) of x[n].
Transcribed Image Text:Let r[n] be the random process that is generated by filtering white noise w[n] ~ N(0, 2) with a discrete-time filter that is designed by applying the bilinear transform to a continuous-time filter. The system function of the continuous-time filter is given as 2(s+1) 3s +1 H(s) = For the sampling period Ta = 2, find the transfer function of the system H(2). а. %3D b. Find the power spectrum Pw(z) of w[n] and Px(z) of x[n].
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