CS2403 DIGITAL SIGNAL PROCESSING ANNA UNIVERSITY QUESTION PAPER NOV/DEC 2010 for IT 7th Semester ...

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

Fifth Semester

Information Technology

CS 2403 â€" DIGITAL SIGNAL PROCESSING

(Regulation 2008)

Time : Three hours Maximum : 100 Marks

Answer ALL questions

PART A â€" (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 â€"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 â€" (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 ( ) ( âˆ' + = n u n u n x n
) 5 ( ) ( âˆ' = 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 [ âˆ' = x
(2) ] 1 , , 0 , [ j j x = when 1 âˆ' = 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
) 1 732 . 1 )( 1 (
1
) (
+ + +
=
s s s
s Ha .
Assume sampling frequency of 100 rad/sec.
Or
 132  132  132 
53110 3
(b) Design FIR filter using impulse invariance technique. Given that
) 6 5 (
1
) (
+ +
=
s s
s Ha
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 :
, 1 ) ( = jw e H 2 / / / π < w
= 0, otherwise.
Or
(b) Draw THREE different FIR structures for the H(z) given below:
) 1 )( 6 5 1 ( ) ( 1 2 1 âˆ' âˆ' âˆ' + + + = 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.