DSP NOV/DEC 2010

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

                             Electronics and Communication Engineering
                          EC 2302 — DIGITAL SIGNAL PROCESSING
                                          (Regulation 2008)
Time : Three hours                                                                            Maximum : 100 Marks
Answer ALL questions

PART A — (10 × 2 = 20 Marks)
1.
Obtain the circular convolution of the following sequences ( ) { } 2,11,=xn ; ( ) { } 22,1, −=hn .
2.
How many multiplications and additions are required to compute N-point  DFT using radix-2 FFT?
3.
What is prewarping?
4.
What is the advantage of direct form II realization when compared to direct form I realization?
5.
Give the equations for Hamming window and Blackman window.
6.
Determine the transversal structure of the system function 
( ) 23 1 3412 −−− −−=+ zzzzH 
7.
What is truncation?
8.
What is product quantization error?
9.
What is decimation?
10.
What is sub band coding?
Question Paper Code : 53123
 
53123 2
PART B — (5 × 16 = 80 Marks)
11.
(a) (i) Compute the eight-point DFT of the sequence 
   ( )   
  = 0 0,0,0,, 2 1 , 2 1 , 2 1 , 2 1 xn 
   Using the radix-2 decimation-in-time algorithm. (10) 
 (ii) Explain overlap-add method for linear FIR filtering of a long sequence.   (6) Or  (b) (i) Compute the eight-point DFT of the sequence  
   ( )
   ≤≤
=
otherwise0, 071, n xn 
   By using the decimation-in-frequency FFT algorithm. (10) 
 (ii) Summarize the properties of DFT. (6)
12.
(a) Determine the system function ( ) Hz of the Chebyshev’s low pass digital filter with the specifications 
 1 dB =p α
 ripple in the pass band
πω 2.00 ≤≤ 
 = s α
 15 dB ripple in the stop band
πω
π ≤≤3.0 
 using bilinear transformation (assume T= 1 sec). (16)
Or  (b) Obtain the direct form I, direct form II, cascade and parallel form realization for the system   ( ) ( ) ( ) ( ) ( ) ( ) 20.613.6230.210.1 −+−++−+−−= xnxnxnynynyn (16)
13.
(a) Design an ideal high pass filter with a frequency response 
 ( )
      
 Find the values of ( ) hn for N =11 using hamming window.   Find ( ) Hz and determine the magnitude response. (16)
Or
 
53123 3
(b) (i) Determine the coefficients ( ) { } hn of a linear phase FIR filter of length M =15 which has a symmetric unit sample response and a frequency response that satisfies the condition (10) 
  

 (ii) Obtain the linear phase realization of the system function 
   ( ) 56 3412 2 1 43 1 3 1 2 1 −− −−−− + 1 ++++=+ zz zzzzHz (6)
14.
(a) Discuss in detail the errors resulting from rounding and truncation. (16)
Or 
(b) Explain the limit cycle oscillations due to product round off and overflow errors.    (16)
15.
(a) Explain the polyphase structure of decimator and interpolator. (16)
Or 
(b) Discuss the procedure to implement digital filter bank using multirate signal processing.   (16)

DSP (ANNA UNIVERSITY) MAY/JUNE 2012 QUESTION PAPER

B.E./B.TECH. DEGREE EXAMINATION, MAY/JUNE 2012 

FIFTH SEMESTER

                                 ELECTRONICS AND COMMUNICATION ENGINEERING 
                                     EC 2302 / EC52 – DIGITAL SIGNAL PROCESSING
                                                              (REGULATION 2008) 

TIME: THREE HOURS                                                                MAX: 100 MARKS 
ANSWER ALL THE QUESTIONS 
PART A – (10 X 2 = 20) 
1. WHAT IS TWIDDLE FACTOR? 
2. HOW MANY STAGES OF DECIMATIONS ARE REQUIRED IN THE CASE OF A 64 POINT RADIX 2 DIT FFT ALGORITHM? 
3. WHY IS THE BUTTERWORTH RESPONSE CALLED A MAXIMALLY FLAT RESPONSE? 
4. WHAT IS FREQUENCY WARPING? 
5. WHAT ARE THE FEATURES OF FIR FILTER DESIGN USING THE KAISER’S APPROACH? 
6. DRAW THE DIRECT FORM IMPLEMENTATION OF THE FIR SYSTEM HAVING DIFFERENCE EQUATION. 
     y(n) = x(n) – 2x(n-1) + 3x(n-2) – 10x(n-6) 
7. WHAT ARE LIMIT CYCLE OSCILLATIONS? 
8. WHAT IS DEAD – BAND OF A FILTER? 
9. WHAT IS DECIMATION? 
10. FIND THE EXPRESSION FOR THE FOLLOWING MULTIRATE SYSTEMS.       
   
                                              PART B – (5 X 16=80) 
11. (a) (i) DIFFERENTIATE DFT FROM DTFT.                                                  (4) 
      (ii) COMPUTE AN 8 POINT DFT OF THE SEQUENCE  x(n)   (1,0,1,-1,1,-1,0,1)                                                                                  (12)  
QUESTION PAPPER CODE: 11332
     4          
24
     4          
[OR]  
     (b) (i) PROVE THAT FFT ALGORITHM HELPS IN REDUCING THE NUMBER OF COMPUTATIONS INVOLVED IN DFT COMPUTATION.                         (6)  
           (ii) COMPUTE A 8 POINT DFT OF THE SEQUENCE USING DIT – FFT ALGORITHM                             X(n)   =(1,2,3,2,1,0)                                                                          (10)                                                                   
12. (a) (i) EXPLAIN THE PROCEDURE FOR DESIGNING ANALOG FILTERS USING THE CHEBYSHEV APPROXIMATION.                                                 (6) 
           (ii)  CONVERT THE FOLLOWING ANALOG TRANSFER FUNCTION IN TO DIGITAL USING IMPULSE INVARIANT MAPPING WITH T = 1 sec.      (10) 
[OR]  
      (b)  (i) DESIGN A DIGITAL SECOND ORDER LOW – PASS BUTTERWORTH FILTER WITH CUT-OFF FREQUENCY  2200 Hz USING BILINEAR TRANSFORMATION. SAMPLING RATE IS 8000 Hz.                      (8) 
            (ii) DETERMINE THE CASCADE FORM AND PARALLEL FORM IMPLEMENTATION OF THE SYSTEM GOVERNED BY THE TRANSFER FUNCTION                                      
                                        (1 + Z -1)(1 – 5Z -1 – Z -2)                     H(Z)=         (1 +2Z -1 + Z -2)(1 + Z -1 + Z -2)                                                       (8) 
13. (a) DESIGN AN FIR LOW PASS DIGITAL FILTER BY USING THE FREQUENCY SAMPLING METHOD FOR THE FOLLOWING SPECIFICATIONS 
CUTOFF FREQUENCY = 1500Hz 
SAMPLING FREQUENCY = 15000 Hz 
ORDER OF THE FILTER : N = 10 
FILTER LENGTH REQUIRED L = N  + 1 = 11                                                     (16) 
[OR] 
(b) (i) EXPLAIN WITH NEAT SKETCH THE IMPLEMENTATION OF FIR FILTERS IN THE  
      (1) DIRECT FORM 
      (2) LATTICE FORM                                                                                             (6) 
      (ii) DESIGN A DIGITAL FIR BAND – PASS FILTER WITH LOWER CUT-OFF FREQUENCY 2000 Hz AND UPPER CUT-OFF FREQUENCY 3200 Hz USING HAMMING WINDOW OF LENGTH N = 7. SAMPLING RATE IS 10000 Hz.                                                                                                                             (10)  
14. (a) (i) WHAT IS QUANTIZATION OF ANALOG SIGNALS? DERIVE THE EXPRESSION FOR THE QUANTIZATION ERROR. 
      (ii) EXPLAIN COEFFICIENT QUANTIZATION IN IIR FILTER. 
[OR] 
     (b) (i) HOW TO PREVENT LIMIT CYCLE OSCILLATION ? EXPLAIN. 
          (ii)WHAT IS MEANT BY SIGNAL SCALING? EXPLAIN.
 
15. (a) (i) EXPLAIN SAMPLING RATE CONVERSION BY A RATIONAL FACTOR AND DERIVE INPUT OUTPUT RELATION IN BOTH TIME AND FR EQUENCY DOMAIN.                                                                                   (10) 
            (ii) EXPLAIN THE MULTISTAGE IMPLEMENTATION OF SAMPLING RATE CONVERSION.                                                                                         (6) 
[OR]  
     (b) (i) EXPLAIN THE DESIGN OF NARROW BAND FILTER USING SAMPLING RATE CONVERSION.                                                                       (8) 
          (ii) EXPLAIN THE APPLICATION OF SAMPLING RATE CONVERSION IN SUB – BAND CODING.                                                                                    (8)