Download Visvesvaraya Technological University (VTU) BE ( Bachelor of Engineering) ECE (Electronic engineering) 2017 Scheme 2020 January Previous Question Paper 5th Sem 17EC52 Digital Signal Processing
i
17EC52
Fifth Semester B.E. Degree Examination, Dec.201

171.ili.2020
Digital Signal Processing
Time: 3 hrs. Max. Marks: 100
Note: Answer ant' FIVE full questions, choosing ONE full question from each module.
Module1
7
7d
.
I)
C3 1 a. Show that finite duration sequence of length L can be reconstructed from the equidistant N
. c
..,.
y
samples of its Fourier transform, where N ?_ L. (06 Marks)
.t.0
s
b.
Compute the 6  point DFT of the sequence x(n)  11, 0, 3, 2, 3, 0}. (08 Marks)
E.. =
3
c.
Find the Npoint DFT of the sequence x(n) = a
n
, 0 _.. n __ N  1. (06 Marks)


t= '
7,
,
:i.
,.7_
OR  _
c r ,
2 a. Determine the 6point sequence x(n) having the DFT
? ,:
X(K) = { 12, 3
.
0 , 0, 0, 0, 3+ jJ } . (08 Marks)
=T. .=, '
= :
b. Derive the equation to express z  transform of a finite duration sequence in terms of its
..,
?
,.. 
au .,
Npoint DFT.
? g
(06 Marks)
c. Compute the circular convolution of the sequences On) = {1, 2, 2, 11 and
x2(n) = 11, 2, 2, 11. (06 Marks)
=
?
5
7 _
Module2
3 a. State and prove the modulation property (multiplication in timedomain) of DFT. (06 Marks)
b. The even samples of an elevenpoint DFT of a real sequence are : X(0) = 8, X(2) = 2 + j3,
,
i._ .
X(4) = 3 j5, X(6) = 4 + j7, X(8) = 5  j9 and X(10) = ..,rs  j2. Determine the odd samples
_ w
O
. 
c
of the DFT.
a. c_
(06 Marks) ,_. ....,
E r


o rj
c. An LTI system has impulse response h(n) = {2, 1, 1}. Determine the output of the system
, (..) ,..:
..... . ,., ?
for the input x(n) = 11, 2, 3, 3, 2, 11 using circular convolution method. (08 Marks)
g ' '"
7
?
3
tt 7 f.,
OR ..=
5
72
4 a. State and prove circular time reversal property of DFT. (06 Marks)
b. Determine the number of real multiplications, real additions, and trigonometric functions
required to compute the 8point DFT using direct method. (04 Marks)
c. Find the output y(n) of a filter whose impulse response is h(n) = {1, 2, 11, and the input is
5 e
?
).
x(n) = {3, 1, 0, 1, 3, 2, 0, 1, 2, 11 using overlap  add method, taking N = 6. (10 Marks)
0<
 rsi
Module3
L.)
5
a. Compute the 8pont DFT of the sequence x(n) = cos(Tcn/4), 0 n 7, using DITFFT
algorithm. (10 Marks)
? c_
b. Given x(n) = 11, 2, 3, 41, compute the DFT sample X(3) using Goestzel algorithm.
(06 Marks)
c.
Determine the number of complex multiplications and complex additions required to
compute 64point DFT using radix.2 FFT algorithm. (04 Marks)
1 of 2
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USN
i
17EC52
Fifth Semester B.E. Degree Examination, Dec.201

171.ili.2020
Digital Signal Processing
Time: 3 hrs. Max. Marks: 100
Note: Answer ant' FIVE full questions, choosing ONE full question from each module.
Module1
7
7d
.
I)
C3 1 a. Show that finite duration sequence of length L can be reconstructed from the equidistant N
. c
..,.
y
samples of its Fourier transform, where N ?_ L. (06 Marks)
.t.0
s
b.
Compute the 6  point DFT of the sequence x(n)  11, 0, 3, 2, 3, 0}. (08 Marks)
E.. =
3
c.
Find the Npoint DFT of the sequence x(n) = a
n
, 0 _.. n __ N  1. (06 Marks)


t= '
7,
,
:i.
,.7_
OR  _
c r ,
2 a. Determine the 6point sequence x(n) having the DFT
? ,:
X(K) = { 12, 3
.
0 , 0, 0, 0, 3+ jJ } . (08 Marks)
=T. .=, '
= :
b. Derive the equation to express z  transform of a finite duration sequence in terms of its
..,
?
,.. 
au .,
Npoint DFT.
? g
(06 Marks)
c. Compute the circular convolution of the sequences On) = {1, 2, 2, 11 and
x2(n) = 11, 2, 2, 11. (06 Marks)
=
?
5
7 _
Module2
3 a. State and prove the modulation property (multiplication in timedomain) of DFT. (06 Marks)
b. The even samples of an elevenpoint DFT of a real sequence are : X(0) = 8, X(2) = 2 + j3,
,
i._ .
X(4) = 3 j5, X(6) = 4 + j7, X(8) = 5  j9 and X(10) = ..,rs  j2. Determine the odd samples
_ w
O
. 
c
of the DFT.
a. c_
(06 Marks) ,_. ....,
E r


o rj
c. An LTI system has impulse response h(n) = {2, 1, 1}. Determine the output of the system
, (..) ,..:
..... . ,., ?
for the input x(n) = 11, 2, 3, 3, 2, 11 using circular convolution method. (08 Marks)
g ' '"
7
?
3
tt 7 f.,
OR ..=
5
72
4 a. State and prove circular time reversal property of DFT. (06 Marks)
b. Determine the number of real multiplications, real additions, and trigonometric functions
required to compute the 8point DFT using direct method. (04 Marks)
c. Find the output y(n) of a filter whose impulse response is h(n) = {1, 2, 11, and the input is
5 e
?
).
x(n) = {3, 1, 0, 1, 3, 2, 0, 1, 2, 11 using overlap  add method, taking N = 6. (10 Marks)
0<
 rsi
Module3
L.)
5
a. Compute the 8pont DFT of the sequence x(n) = cos(Tcn/4), 0 n 7, using DITFFT
algorithm. (10 Marks)
? c_
b. Given x(n) = 11, 2, 3, 41, compute the DFT sample X(3) using Goestzel algorithm.
(06 Marks)
c.
Determine the number of complex multiplications and complex additions required to
compute 64point DFT using radix.2 FFT algorithm. (04 Marks)
1 of 2
17EC5:
OR
6 a. Determine the sequence x(n) corresponding to the 8point DFT
X(K) = (4, 1?j2.414, 0, 1?j0.414, 0, 1+j0.414, 0, 1+j2.414} using DIFFFT algorithm.
(10 Marks)
b. Draw the signal flow graph to compute the 16point DFT using DITFFT algorithm.
(04 Marks)
c. Write a short note on Chirp?z transform. (06 Marks)
Module4
7 a. Draw the direct form I and direct form II structures for the system given by :
z
I
?3z
2
H(z)= (08 Marks)
1+4z
1
+ 2z
2
0.5z
3
?
b. Design a digital Butterworth filter using impulse?invariance method to meet the following
specifications :
0.8 .IFI(co)I__1, (;4 (o< 0.2n
IH(6))1
0.2, 0.67c 5.. o)
Assume T = 1. (12 Marks)
OR
8 a. Draw the cascade structure for the system given by :
H(z)=
(z1)(z ?3)(z
2
+ 5z + 6)
(z
2
+ 6z + 5)(z

? 6z + 8)
(08 Marks)
b. Design a type1 Chebyshev analog filter to meet the following specifications :
H(Q) I dB 5. 0, 0 f2 < 1404R rad/sec
H(n) I dB ?60, SI 8268nrad/sec
(12 Marks)
Module5
9 a. Realize the linear phase digital filter given by :
H(z)=1+ ?
1
z
I
j + z
2
+ ?
2
z
3 1.
+z4
1

2 3 5 3
(06 Marks)
b. List the advantages and disadvantages of FIR filter compared with IIR filter. (04 Marks)
c. Determine the values of h(n) of a detail low pass filter having cutoff frequency coc = 7E/2 and
length M = 11. Use rectangular window. (10 Marks)
OR
10 a. An FIR filter is given by : y(n) = x(n)+
5
2
x(n ?1) +
4
3
x(n ? 2) +
3

1
x(n ?3) . Draw the Lattice
structure. (06 Marks)
b. Determine the values of filter coefficients h(n) of a high?pass filter having frequency
response :
H
d
(e"" ) =1,
4
?
it
1 o) It
=0, IwI<
4
Choose M = 11 and use Hanning windows. (10 Marks)
c.
Write the time domain equations, widths of main lobe and maximum stop band attenuation
of Bartlett window and Hanning window.
.
(04 Marks)
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This post was last modified on 02 March 2020