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JUP – 017

*JUP017*

II Semester M.E. (Control & Instrumentation) Degree Examination, January/February 2014 (2K8 Scheme) CI– 21 : ADAPTIVE SIGNAL PROCESSING (Elective) Time : 3 Hours

Max. Marks : 100

Instruction: Answer any five full questions. 1. a) Explain the lattice predictor with neat diagram. b) Explain the factors to be considered for chosing the algorithm for operation. 2. a) Evaluate the transfer function of Auto-regressive model.

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b) Consider an auto regressive process u (n) of order two described by the difference equation u (n) = u (n – 1) – 0.5 u (n – 2) + v (n) where v (n) is white noise with zero mean and variance 0.5. i) Write the Yule Walker Equations for the process. ii) Solve there two equations for auto correlation function values r (1) and r (2). 10 3. a) Prove that for the cost function J to attain its minimum value the estimation error e0 (n) should be orthogonal to each input sample. 10 b) Prove that Jmin = σ 2d − pHR −1P . 4. a) Derive the equation for forward prediction error filter. b) Derive the equation PM = r(o) – rBT Wb the backward prediction error power. 5. a) Explain the Cholesky factorization. b) Explain the order update recursions for the prediction errors. 6. a) Explain the principles of Joint process estimation. b) Derive the LMS algorithm.

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7. a) Explain how adaptive signal processing is used in radar system. b) Explain how adaptive signal processing is used in economic processes. ______________

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