JE – 1000

*JE1000*

II Semester M.E. (Control and Instrumentation) Degree Examination, July/Aug. 2013 2K8 CIEL 21 Elective – II : ADAPTIVE SIGNAL PROCESSING Time : 3 Hours

Max. Marks : 100

Instruction : Answer any five full questions.

1. a) Explain the Transversal filter with neat diagram.

8

b) Briefly explain the four basic classes of adaptive filtering applications.

12

2. a) Derive the necessary and sufficient condition for the process u(n) to mean ergodic in the mean-square-error sense.

10

b) Consider a MA process x(n) of order two described by the difference equation x(n) = v(n) + 0.7 v(n–1)+0.25 v(n–2) where v(n) is a zero-mean white noise process of unit variance. The requirement is to approximate this process by AR process u(n) of order M. Do the approximation for the following orders a) M = 2 b) M = 5 c) M = 10

10

3. a) Evaluate the transfer function of following stochastic models. i) The MA Model ii) ARMA Model

10

b) Derive Yule-Walker equations.

10

4. a) Derive Weiner-Hopf equations and formulate them in Matrix form.

8

b) Derive the equation relating forward and backward predictors.

4

c) Explain the Levinson Peirbin algorithm and prove that PM = Po M

π M−1

(1− | KM |2 ).

8

P.T.O.

*JE1000*

JE – 1000 5. a) Explain the Cholesky factorization.

8

b) Explain the order update recursions for prediction errors. ⎡4 3 6. a) Find the eigen values of R and its normal form if R = ⎢⎢ 3 6 ⎢⎣ 0 2

b) Explain Joint process estimation. 7. Write short notes on :

12 0⎤ 2⎥ . ⎥ 4 ⎥⎦

10

10 (5×4=20)

i) Systolic array ii) Predictive speech model iii) Approaches to develop linear adaptive filters iv) Applications of adaptive filters.

____________

ADAPTIVE SIGNAL PROCESSING.pdf

Write short notes on : (5×4=20). i) Systolic array. ii) Predictive speech model. iii) Approaches to develop linear adaptive filters. iv) Applications of adaptive filters.

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