Visvesvaraya Technological University (VTU) 2006 B.E Fifth Semester , .06 / 07 Digital Signal Processing - Question Paper

Fifth Semester B.E. Degree exam , Dec.06 / Jan. 07
Electrical and Electronics Engineering
Digital Signal Processing
Time:3 hrs] [Max.Marks:100
Note: ans any 5 ques..
1. a. Determine eight point DFT of the sequence x(n) = { 1, 1, 1, one } .Sketch its
magnitude and phase spectra.
(10Marks)
b. obtain ‘N’ point DFT of the sequence x(n) = e jwmn . 0 £ n £ N1.
(05 Marks)
c. five samples of the eight point DFT X(K) are X(O) = 0.25,
X(1) = 0.125j
0.3018, X(6)= X(4) = 0, X(5) = 0.125 – j 0.0518. (05 Marks)
2. a. g(n) and h(n) are 2 sequences of length 6. They have six point DFT’s G(k)
and H(k) respectively .G(n) and H(k) = { 4.1, 3.5, 1.2, 5, 2, 3.3 }
The DFT’s G(k) and H(k) are related by circular frequency shift as
H(k)=G((k3))
6. Determine h(n) without computing IDFT. (08 Marks)
b. A long sequence x(n) is filtered through a filter of impulse response h(n) to
provide output y(n) . calculate y(n) using overlap add technique. provided x(n)
h(n) as follows.
x(n) = { 1, 2, 0, 3,
4, 2, 1,
1, 2,
3, 2, 1, 3
}
h(n) = { 1, 1, 1}. Use six point circular convolution. (12 Marks)
3. a. provided x(n) = n+1 and N =8, determine x(k) using DIFFFT
algorithm. Mark
all intermediate outputs and write all necessary equations. (10 Marks)
b. Derive and draw the complete decimation – in time (DIT) signal flow graph
to calculate DFT of a six point sequence. Mark all intermediate outputs and
write corresponding calculations. (10 Marks)
4. a. Realize the system function H(Zz) in cascade and parallel form.
úû
ù
êë
úû é +
ù
êë
ú é -
û
ù
ê
ë
é
÷
ø
ö
ç
è
ú - æ -
û
ù
ê
ë
é
÷
ø
ö
ç
è
- æ +
- - +
=
2 two four 4
1
2 2
1
( ) ( 1) ( two )( 1)
Z j Z j Z j Z j
H Z Z Z Z Z (14 Marks)
b. Realize the FIR filter having impulse response
( four ) ( 5)
4
( 3) 1
2
( two ) 1
2
( 1) 1
4
h ( n ) = d ( n ) - one d n - + d n - + d n - - d n - + d n -
Use minimum number of multipliers. (10 Marks)
5. a. Design a Butterworth analog highpass filter that will meet the subsequent
specifications :
(i) Maximum pass band attenuation = 2dB
(ii) Pass band edge frequency = 200 rad /sec
(iii) Minimum stop band attenuation = 20dB
(iv) Stop band edge frequency = 100 rad / sec (10 Marks)
b. Determine the system function H(z) of the least order chebyshev filter that
meets the subsequent specifications.
(i) three dB ripple in the pass band 0 £ W £ 0. 3p .
(ii) At lowest 20 dB attenuation in the stop band 0 .6 p £ W £ p .
Use Bilinear transformation.
6. a. discuss Impulse Invariant Transformation. (08 Marks)
b. A digital low pass filter is needed to meet the specifications:
20 ( ) 0. six 13. nine 794 .
20 log ( ) 0. two 1. nine 328
Log H W w dB
H W w dB
= ³ -
= ³ -
p
p
Filter must have a maximally flat frequency response. obtain H (Z) using
Impulse invariant transformation. (12 Marks)
7. a. A filter is to be designed with the subsequent desired frequency response.
4 4
( ) 0
p p
H W = - < W < d
p
p
= e - j w < W <
4
2
obtain the frequency response of the FIR filter designed using rectangular window.
W ( n ) = one R 0 £ n £ 4
= 0 otherwise (10 Marks)
b. A low pass filter has the desired frequency response
Hd ( w ) = Hd ( e jw ) 0 < w< p / 2
= 0 p/2 < w < p .
Determine h(n) based on frequency sampling technique , Use N = 7. (10 Marks)
8. Write notes on :
a. DSP architecture (TMS 320 c5 x processes) (08 Marks)
b. Advantages and disadvantages of frequency sampling design. (06 Marks)
c. Advantages and disadvantages of IIR and FIR filters.

Earning:   Approval pending.