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M.E. DEGREE EXAMINATION, JANUARY 2011

First semester

Applied Electronics

248101 ADVANCED DIGITAL SIGNAL PROCESSING

(Common to M.E Communication Systems and M.E. Computer and Communication)

(Regulation 2009)

Time: Three hours Maximum: 100 marks

Answer ALL the Questions

PART A(10 2 = 20 marks)

1. Define: Ensemble averaging with an example.

2. State Parsevals theorem.

3. Define periodogram.

4. Write the Yule- Walker equation for a ARMA (p,q) process.

5. What is the use of a Wiener smooting filter?

6. Write the minimum error equation obtained in Pronys method.

7. What is need for an adaptive filter?

8. Compare the adaptive noise cancellation and adaptive echo cancellation.

9. List out some applications of multirate signal processing.

10. Multistage implementation of Multirate system will reduce the computational complexity at

each stage. Justify.

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PART B(5 16 = 80 marks)

11. (a) A linear shift invariant system is described by the transfer function

H(z)=(1-0.5 z-1)/(1-0.33 z-1) which is excited by zero mean exponentially correlated noise x(n) with an

auto correlation sequence rk(k)=(0.5)|k|

Let y(n) be the output process, y(n) = x(n)*h(n). Determine the

(i) Power spectrum (z)P y of y(n)

(ii) Auto correlation sequence of y(n)

(iii) Cross correlation sequence between x(n) and y(n)

(iv) Cross power spectral density P xy(z). (16)

Or

(b) (i) Explain briefly about ergodic process with necessary equations and also state the mean ergodic

theorems. (10)

(ii) The power spectrum of a wide sense stationary process x(n) is given as Px (e(2524 cos )/ (26-

10 cos ). Find the whitening filter H(z) that produces unit variance white noise when the input is x(n).

(6)

12. (a) With necessary derivation, explain the periodogram averaging using Bartletts method and

compare the same with the Welch method of periodogram averaging. (16)

Or

(b) (i) Consider that Bartletts method is used to estimate the power spectrum of a process from a

sequence of N = 2000 samples.

(1) What is the minimum length L that may be used for each sequence to

0.005?

(2) Explain why it would not be advantageous to increase L beyond the value found in (I)

(3) The quality factor of a spectrum estimate is defined to be the inverse of the variability Q =1/v.

Using Bartletts method, what is the minimum number of data samples, N that are necessary to

factor that is 5 times larger than that of the

periodogram? (6)

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(ii) Given the autocorrelation sequence, rx(0)=1, rx(1)=0.8, rx(2)=0.5, rx(3)=0.1. Determine the

for j = 1, 2 ,3 using Levinson Durbin recursion. (10)

13. (a) (i) With necessary equations and neat sketches, explain the pole zero modeling using the , the

model parameters aj (k) and the modeling errors j

(ii) Consider the signal x(n) consisting of a single pulse of X(n)=1; n=0,1,N-1; Use Pronys method to

model x(n) as a unit sample response of a linear shift invariant filter having one pole and one zero.

(8)

Or

(b) (i) Starting from the basic principles, derive the expression for minimum error for a FIR Wiener

filter in terms of autocorrelation matrix Rx and cross correlation vector rdx. (8)

(ii) With necessary expressions, briefly explain about the discrete Kalman filter. (8)

14. (a) (i) With a neat block diagram, explain the operation of an adaptive channel equalizer. (8)

(ii) Show that the normalized LMS algorithm is equivalent for using the update equation

Wn+1=Wn+e' (n)x*(n) where e(n) is the error at time n that is based on the new filter coefficients

Wn+1, e' (n)=d(n)-w n+lX(n). Discuss the relationship between and the parameter e in the

normalized LMS algorithm. (8)

Or

(b) Derive the expression for minimizing the weighted least squares error using Recursive Least

squares algorithm and compare the RLS algorithm with sliding window RLS algorithm. (16)

15. (a) (i) With neat sketches and necessary equations, briefly explain the time domain and

frequency domain characterization of a down sampler with an integer factor of M. (12)

(ii) Write short notes on Wavelet transformation. (4)

Or

(b) (i) Obtain the polyphase decomposition of factor of 3 decimator using a 9-tap FIR lowpass filter

with symmetric impulse response. (8)

(ii) With a neat block diagram, briefly explain about the subband coding of speech signals. (8)

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