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  3. 7 consider an ar1 random process xn generated using a...

Question: 7 consider an ar1 random process xn generated using a...

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7. Consider an AR(1) random process, x[n] generated using a recursive manner as follows: 152 9Random Signals, Wiener Filtering and Speech Coding where 11n] is a white random process with zero-mean with variance σ:L (a) What is run]? What is rx[O],rx[1 and rx[2] (b) LMMSE optimal predictor for this random process is obtained using the or thogonality principle. What is the orthogonality principle? (c) The LMMSE predictor is n 0.8x[n - 1]. What should be the value of the parameter α? Use the orthogonality principle to determine α? (d) Let x[n] aix(n-1] + a-xln-2]. Determine al and a2 using the orthogonality principle. (e) What are the impulse responses of the predictors in parts (c) and (d)?

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