Let x[n] be the random process that is generated by filtering white noise wn] ~ N...

 

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Let x[n] be the random process that is generated by filtering white noise wn] ~ 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(2) of x[n]. с. Find the autocorrelation sequence r(k) of x[n]. Bilinear Transform Definiton : H(z) = H(s) 2 1- z-1 S= Ta 1+z-1 Let x[n] be the random process that is generated by filtering white noise wn] ~ 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(2) of x[n]. с. Find the autocorrelation sequence r(k) of x[n]. Bilinear Transform Definiton : H(z) = H(s) 2 1- z-1 S= Ta 1+z-1