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M.TECH DEGREE EXAMINATIONSecond SemesterBranch : Applied Electronics and Instrumentation; Specialization : Signal Processing

MAESP 201 ADVANCED DIGITAL SIGNAL PROCESSING(2011 admission onwards)

[Regular]

MODEL QUESTION PAPER

Time: Three Hours Maximum Marks : 100

1. a) Derive the Yule Walker equation for an AR process of order M. Show that givenautocorrelation coefficients r(0), r(1), . . . , r(M) we can derive the AR parameters.Find this relationship. (15 marks)

b) Find the relationship of the variance of the zero mean white noise input to the LTI(linear time invariant) system with the AR parameters and autocorrelation coefficientsof the AR process. (10 marks)

Or

2. a) Derive the Wiener-Hopf equations for Linear Transversal filter. Express the matrixformulation of the Wiener-Hopf equations. (20 marks)

b) Draw the Linear Transversal filter for the Wiener filter. (5 marks)

3. a) Explain the steepest descent algorithm applied to the Wiener filter. Derive the updateequation. (10 marks)

b) Draw the structure of the adaptive transversal filter for the steepest descent algorithm.Also draw the bank of cross correlators for computing the corrections to the elementsof the tap-weight vector at time n. (5 marks)

c) State the condition on the step-size parameter for stability or convergence of the steepestdescent algorithm. (5 marks)

d) Explain the Newtons method for optimization. (5 marks)

Or

4. a) Explain the LMS (least mean square) algorithm. (10 marks)

b) For the LMS filter draw the(i) block diagram of the adaptive transversal filter.(ii) detailed structure of the transversal filter component.(iii) detailed structure of the adaptive weight control mechanism.

(6 marks)

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c) Define misadjustment in the context of LMS algorithm. (4 marks)

d) What are the restrictions on the step size parameter for convergence of the LMSalgorithm. (5 marks)

5. a) Write the augmented Wiener-Hopf equations for forward linear prediction. (5 marks)

b) Write the Levinson Durbin recursion. (10 marks)

c) What are some of the advantages of Levinson Durbin recursion. (4 marks)

d) Consider a real valued wide sense stationary signal with autocorrelation values

r(0) = 1, r(1) = 0.5, r(2) = 0.5, r(3) = 0.25

Use Levinson Durbin recursion to solve the augmented Weiner-Hopf equation (equiva-lently the autocorrelation normal equations) and find a third order forward predictionerror filter. (6 marks)

Or

6. a) Explain the RLS (recursive least squares) algorithm with the exponential weightingfactor (or forgetting factor). Write down the update equations for the tap-weightvector. (20 marks)

b) Write the matrix inversion lemma (Woodburys identity). (5 marks)

7. Write notes on the following topics of non-linear signal processing :

a) Non-Gaussian models. (5 marks)

b) Generalized Gaussian distributions. (10 marks)

c) Stable distributions. (10 marks)

Or

8. Write notes on the following topics of non-linear signal processing :

a) Median smoothers. (7 marks)

b) Rank/Order filters. (9 marks)

c) Weighted Median smoothers. (9 marks)

[4 25 = 100 marks]

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