Let x[n] be an iid white standard normal process and define the random process y[n] =...

 

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Let x[n] be an iid white standard normal process and define the random process y[n] = x[n] + x [n-1]. (a) Let a[n] (x[n], x[n 1]) and specify the PDF of a[n]. (b) Calculate y[n] and p[n]. (c) Calculate the autocorrelation of y[n]. (d) Is y[n] wide-sense stationary? Justify your answer. If yes, calculate its PSD. (e) Let b[n] (x[n],y[n]) and sketch the support of fun] (b). = (f) Perform a 2-D variable transformation from a[n] to b[n] in order to calculate the PDF of b[n]. (g) Find the marginal PDF of y[n]. What type of distribution is this? Hint: Sveds 2' t>0 Let x[n] be an iid white standard normal process and define the random process y[n] = x[n] + x [n-1]. (a) Let a[n] (x[n], x[n 1]) and specify the PDF of a[n]. (b) Calculate y[n] and p[n]. (c) Calculate the autocorrelation of y[n]. (d) Is y[n] wide-sense stationary? Justify your answer. If yes, calculate its PSD. (e) Let b[n] (x[n],y[n]) and sketch the support of fun] (b). = (f) Perform a 2-D variable transformation from a[n] to b[n] in order to calculate the PDF of b[n]. (g) Find the marginal PDF of y[n]. What type of distribution is this? Hint: Sveds 2' t>0