**B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2010**

Fifth Semester

Information Technology

CS 2403 — DIGITAL SIGNAL PROCESSING

(Regulation 2008)

Time : Three hours Maximum : 100 Marks

Answer ALL questions

PART A — (10 × 2 = 20 Marks)

Fifth Semester

Information Technology

CS 2403 — DIGITAL SIGNAL PROCESSING

(Regulation 2008)

Time : Three hours Maximum : 100 Marks

Answer ALL questions

PART A — (10 × 2 = 20 Marks)

1. Calculate the minimum sampling frequency required for ( ) 0.5 sin 50 x t t π =

+ 0.25 t π 25 sin , so as to avoid aliasing.

2. State any two properties of Auto correlation function.

3. Write down DFT pair of equations.

4. Calculate % saving in computing through radix –2, DFT algorithm of DFT

coefficients. Assume N = 512.

5. What are the limitations of Impulse invariant method of designing digital

filters?

6. Draw the ideal gain Vs frequency characteristics of :

(a) HPF and

(b) BPF.

7. Compare FIR filters and FIR filters with regard to :

(a) Stability and

(b) Complexity

8. Represent decimal number 0.69 in fixed point representation of length

N = 6.

9. Prove that up sampling by a factor M is time varying system.

10. State a few applications of adaptive filter.

**PART B — (5 × 16 = 80 Marks)**

11. (a) (i) Find the convolution ) ( * ) ( n h n x , where

) ( ) ( n u a n x n =

) ( ) ( n u n h n β =

(ii) Find the Z-transform of the following sequences :

) 1 ( ) ( ) 5 . 0 ( ) ( − + = n u n u n x n

) 5 ( ) ( − = n n x δ .

Or

(b) (i) State and explain sampling theorems.

(ii) Find the Z-transform auto correlation function.

12. (a) (i) Explain, how linear convolution of two finite sequences are obtained

via DFT.

(ii) Compute the DFT of the following sequences :

(1) ] 0 , 1 , 0 , 1 [ − = x

(2) ] 1 , , 0 , [ j j x = when 1 − = j .

Or

(b) Draw the flow chart for N = 8 using tadix-2, DIF algorithm for finding

DFT coefficients.

13. (a) Design digital low pass filter using Bilinear transformation, Given that

Assume sampling frequency of 100 rad/sec.

Or

(b) Design FIR filter using impulse invariance technique. Given that and implement the resulting digital filter by adder, multipliers and

delays Assume sampling period T = 1 sec.

14. (a) Design the first 15 coefficients of FIR filters of magnitude specification is

given below :

Or

(b) Draw THREE different FIR structures for the H(z) given below:

) 1 )( 6 5 1 ( ) ( 1 2 1 − − − + + + = z z z z H .

15. (a) (i) A signal } 1 , 2 , 7 , 5 , 1 , 6 { ) ( = n x

Find :

(1) ) 2 / (n x

(2) ) 2 ( n x .

(ii) Explain any one application using multirate processing of signals.

Or

(b) Write short notes on the following :

(i) Adaptive filter

(ii) Image Enhancement

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