Download VTU BE 2020 Jan ECE Question Paper 17 Scheme 5th Sem 17EC52 Digital Signal Processing

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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.
Module-1

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7
7d
.

I)

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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)

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.t.0
s
b.
Compute the 6 - point DFT of the sequence x(n) -- 11, 0, 3, 2, 3, 0}. (08 Marks)
E.. =

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3
c.
Find the N-point DFT of the sequence x(n) = a
n
, 0 _.. n __ N - 1. (06 Marks)

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---
-
t= '
7,

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,
:i.
,.7_
OR - _
c r ,

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2 a. Determine the 6-point sequence x(n) having the DFT
? ,--:
X(K) = { 12, -3-
.
0 , 0, 0, 0, -3+ jJ } . (08 Marks)

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=T. .=-, '
= -:-
b. Derive the equation to express z - transform of a finite duration sequence in terms of its

..,

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?
,.. -
au .,
N-point DFT.
? g

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(06 Marks)
c. Compute the circular convolution of the sequences On) = {1, 2, 2, 11 and
x2(n) = 1-1, -2, -2, -11. (06 Marks)
=
?

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5
7 _
Module-2
3 a. State and prove the modulation property (multiplication in time-domain) of DFT. (06 Marks)
b. The even samples of an eleven-point DFT of a real sequence are : X(0) = 8, X(2) = -2 + j3,

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,
-i.-_- .
X(4) = 3 -j5, X(6) = 4 + j7, X(8) = -5 - j9 and X(10) = ..,rs - j2. Determine the odd samples
_ w
O-

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. -
c
of the DFT.
a. c_
(06 Marks) ,_. ....,

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E r-
-
-
o rj
c. An LTI system has impulse response h(n) = {2, 1, -1}. Determine the output of the system

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, (..) ,..:-
..... . ,., ?-
for the input x(n) = 11, 2, 3, 3, 2, 11 using circular convolution method. (08 Marks)
g ' '"
7

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?
3

tt 7 f.,
OR ..=

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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 8-point DFT using direct method. (04 Marks)

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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)

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0<
- rsi
Module-3
L.)
5

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a. Compute the 8-pont DFT of the sequence x(n) = cos(Tcn/4), 0 n 7, using DIT-FFT
algorithm. (10 Marks)
? c_
b. Given x(n) = 11, 2, 3, 41, compute the DFT sample X(3) using Goestzel algorithm.
(06 Marks)

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c.
Determine the number of complex multiplications and complex additions required to
compute 64-point 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
-

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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.
Module-1

--- Content provided by‌ FirstRanker.com ---

7
7d
.

I)

--- Content provided by‍ FirstRanker.com ---

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)

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.t.0
s
b.
Compute the 6 - point DFT of the sequence x(n) -- 11, 0, 3, 2, 3, 0}. (08 Marks)
E.. =

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3
c.
Find the N-point DFT of the sequence x(n) = a
n
, 0 _.. n __ N - 1. (06 Marks)

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---
-
t= '
7,

--- Content provided by‌ FirstRanker.com ---

,
:i.
,.7_
OR - _
c r ,

--- Content provided by​ FirstRanker.com ---

2 a. Determine the 6-point sequence x(n) having the DFT
? ,--:
X(K) = { 12, -3-
.
0 , 0, 0, 0, -3+ jJ } . (08 Marks)

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=T. .=-, '
= -:-
b. Derive the equation to express z - transform of a finite duration sequence in terms of its

..,

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?
,.. -
au .,
N-point DFT.
? g

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(06 Marks)
c. Compute the circular convolution of the sequences On) = {1, 2, 2, 11 and
x2(n) = 1-1, -2, -2, -11. (06 Marks)
=
?

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5
7 _
Module-2
3 a. State and prove the modulation property (multiplication in time-domain) of DFT. (06 Marks)
b. The even samples of an eleven-point DFT of a real sequence are : X(0) = 8, X(2) = -2 + j3,

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,
-i.-_- .
X(4) = 3 -j5, X(6) = 4 + j7, X(8) = -5 - j9 and X(10) = ..,rs - j2. Determine the odd samples
_ w
O-

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. -
c
of the DFT.
a. c_
(06 Marks) ,_. ....,

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E r-
-
-
o rj
c. An LTI system has impulse response h(n) = {2, 1, -1}. Determine the output of the system

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, (..) ,..:-
..... . ,., ?-
for the input x(n) = 11, 2, 3, 3, 2, 11 using circular convolution method. (08 Marks)
g ' '"
7

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?
3

tt 7 f.,
OR ..=

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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 8-point DFT using direct method. (04 Marks)

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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)

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0<
- rsi
Module-3
L.)
5

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a. Compute the 8-pont DFT of the sequence x(n) = cos(Tcn/4), 0 n 7, using DIT-FFT
algorithm. (10 Marks)
? c_
b. Given x(n) = 11, 2, 3, 41, compute the DFT sample X(3) using Goestzel algorithm.
(06 Marks)

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c.
Determine the number of complex multiplications and complex additions required to
compute 64-point DFT using radix.2 FFT algorithm. (04 Marks)
1 of 2
17EC5:

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OR
6 a. Determine the sequence x(n) corresponding to the 8-point DFT
X(K) = (4, 1?j2.414, 0, 1?j0.414, 0, 1+j0.414, 0, 1+j2.414} using DIF-FFT algorithm.
(10 Marks)
b. Draw the signal flow graph to compute the 16-point DFT using DIT-FFT algorithm.

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(04 Marks)
c. Write a short note on Chirp?z transform. (06 Marks)
Module-4
7 a. Draw the direct form I and direct form II structures for the system given by :
z

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-I
?3z
-2

H(z)= (08 Marks)

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1+4z
-1
+ 2z
-2
-0.5z

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-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

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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 :

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H(z)=
(z-1)(z ?3)(z
2
+ 5z + 6)
(z

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2
+ 6z + 5)(z
-
? 6z + 8)
(08 Marks)

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b. Design a type-1 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)

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Module-5
9 a. Realize the linear phase digital filter given by :
H(z)=1+ ?
1
z

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-I
j + -z
-2
+ ?
2

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z
-3 1.
+z-4
1
-

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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)

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OR
10 a. An FIR filter is given by : y(n) = x(n)+-
5
2
x(n ?1) +

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4
3
x(n ? 2) +
3
-

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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 :

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H
d
(e"" ) =1,
4

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?
it
1 o) It
=0, IwI<
4

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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.

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.
(04 Marks)
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