Consider an MA process x(n) of order two described by the difference equation x(n) = v(n)...

 

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Consider an MA process x(n) of order two described by the difference equation x(n) = v(n) + 0.75 v(n – 1) + 0.75 v(n – 2), | where v(n) is a zero-mean white-noise process of unit variance. The requirement is to approximate this process by an AR process u(n) of order M. Do this approximation for the following orders: (а) М3 2. (b) М35. (с) М%3D 10. Comment on your results. How big would the order M of the AR process u(n) have to be for it to be equivalent to the MA process x(n) exactly? Consider an MA process x(n) of order two described by the difference equation x(n) = v(n) + 0.75 v(n – 1) + 0.75 v(n – 2), | where v(n) is a zero-mean white-noise process of unit variance. The requirement is to approximate this process by an AR process u(n) of order M. Do this approximation for the following orders: (а) М3 2. (b) М35. (с) М%3D 10. Comment on your results. How big would the order M of the AR process u(n) have to be for it to be equivalent to the MA process x(n) exactly?

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