Question: 5. Let Yn = (Xn+1 + Xn + X.,-1)/3, which is a smoothed form of Xn. a) Find the impulse response and transfer function of

5. Let Yn = (Xn+1 + Xn + X.,-1)/3, which is

5. Let Yn = (Xn+1 + Xn + X.,-1)/3, which is a smoothed form of Xn. a) Find the impulse response and transfer function of the corresponding smoothing filter. b) Find autocorrelation function Ry (k) and power spectral density Sy() of Y. Find E[Y,2). c) Suppose X, is a white noise process with variance op. Find the joint pmf for (Y, Yn+1, Yn+2). 5. Let Yn = (Xn+1 + Xn + X.,-1)/3, which is a smoothed form of Xn. a) Find the impulse response and transfer function of the corresponding smoothing filter. b) Find autocorrelation function Ry (k) and power spectral density Sy() of Y. Find E[Y,2). c) Suppose X, is a white noise process with variance op. Find the joint pmf for (Y, Yn+1, Yn+2)

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