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)