Question: Let X (t) is zero-mean, stationary, Guassian process with autocorrelation function RX (). This process is applied to a square-law device, which is obtained by

Let X (t) is zero-mean, stationary, Guassian process with autocorrelation function RX (τ). This process is applied to a square-law device, which is obtained by the input-output relation Y (t) = X2 (t), where Y (t) is the output

(a) Show that the mean of y (t) is RX (0).

(b) Show that the auto covariance function of Y (t) is 2R2X (τ).

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