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R. No. :

M.E./M.Tech. DEGREE EXAMINATION, JUNE 2011.

Common to M.E. Applied Electronics/M.E. Computer and Communication/

M.E. Communication Systems

First Semester

248101 ADVANCED DIGITAL SIGNAL PROCESSING

(Regulation 2010)

Time : Three hours Maximum : 100 marks

Answer ALL questions.

PART A (10 2 = 20 marks)

1. Write Yule-Walker equation.

2. The power density spectrum of an AR process ( ){ }nx is given as

( ) ( )2

22

2

2

11

25

wjjw

wxx

eewAw

+

==

where2w is the variance of the input

sequence. Determine the difference equation for generating the AR process

when the excitation is white noise.

3. Define Periodogram? How can it be smoothed?

4. Compare Parametric and Non-Parametric methods of spectral estimation.

5. How do find the ML estimate?

6. Write the error criterion for LMS algorithm.

7. Why are FIR filters widely used for adaptive filters?

8. Express the LMS adaptive algorithm. State its properties.

9. What are the advantages of multistage implementation in multirate signal

processing?

10. What is purpose of low pass filter before the down sampler?

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PART B (5 16 = 80 marks)

11. (a) (i) Let x(n) be a stationary random process with zero mean and

autocorrelation rx(k)if the processy(n) = x(n) f(n).wheref(n)is the

deterministic sequence. Find the mean my(n) and autocorrelation

ry(k,l)of the processy(n). (5)

(ii) State and prove Parsevals Theorem. (5)

(iii) What do mean stationary of a random process? Explain with an

example. (6)

Or

(b) (i) Obtain Wiener Khintchines relation. (8)

(ii) Define power spectral density and list the methods of computing

the power spectral density for stationary random process. (8)

12. (a) (i) Consider the ARMA process generated by the difference equation

( ) ( ) ( ) ( ) ( )19.026.016.1 ++= nwnwnxnxnx

(1) Determine the system function of the whitening filter and its

poles and zeros.

(2) Determine the power density spectrum of ( ){ }nx . (8)

(ii) Show that Barlett estimate of the power spectral density is

asymptotically unbiased, the variance of the estimate decrease with

the number of data sections and spectrum estimates are consistant.

(8)

Or

(b) (i) Explain the Levinson Durbin Recursion algorithm for solving

Toplitz system of equations using an AR model. (8)

(ii) How the Levison equation is used to derive the lattice filterstructure for FIR digital filters? (8)

13. (a) (i) What is kalman filter? Explain its features. (8)

(ii) Give applications where Kalman filter is used. (8)

Or

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(b) (i) Explain how AR parameters are obtained using Linear Prediction.

(8)

(ii) Use the Levinson recursion to find the predictor polynomial

corresponding to the auto correlation sequence R = [2,1,1,2]T. (8)

14. (a) Justify the use of adaptive filters instead of conventional filters in

applications such as

(i) Noise cancellation

(ii) Channel equalization. (16)

Or

(b) Obtain Widrow-Hopf LMS algorithm. (16)

15. (a) (i) What is the need of multirate signal processing? Give few

applications. (4)

(ii) Explain the interpolation process in time domain and frequency

domain. (12)

Or

(b) (i) Describe about sub band coding. (8)

(ii) Design a two-stage decimator for the following specifications.

100= , Pass band : 500 , Transition band : ,5550

Ripple : 11 10

= 32 10

= , Input sampling rate : 10,000 Hz. (8)