Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 7th Sem New 2170914 Digital Signal Processing Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2170914 Date: 15/11/2018
Subject Name: Digital Signal Processing
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) A discrete ?time signal x(n) is given below :
X(n) = {1,2,1,-2,1,2,3,4,14}
?
Sketch and label carefully each of the following signals:
(i) x(n-2) (ii) x(-4-n) (iii) x(n/2)
(b) List advantages of Digital Signal Processing over Analog
Signal Processing.
(c) Find the linear convolution of following pairs of discrete
sequences
(i) x
1
(n) = {1,2,3,4,12,4,6} h
1
(n) = {4,3,2,1}
(ii) x
1
(n) = {1,2,1,2,1,2,1} h
1
(n) = {1,2,3,4,3,2,1}
MARKS
03
04
07
Q.2 (a) Obtain Fourier transform of single sided exponential pulse 03
x(n) = a
n
u(n)
(b) Check the following systems for time invariance and 04
Linearity : (i) y(n) = n[x(n)]
2
(ii) y(n) = a[x(n)]
2
+b x(n)
(c) Calculate DTFT of following signals 07
(i) x(n) = [ ? ,?, ?, ? ] (ii) x(n) = 2( ? )
n
u(n)
OR
(c) Explain Inverse system, minimum phase system and all pass 07
system. Determine Inverse of the system characterized by
y(n)=0.5y(n-1)+x(n) assuming zero initial conditions.
Q.3
(a)
Find the Z Transform of u(n-1)
03
(b) The impulse response of the LTI system is h(n)={2,4,5,6}. 04
?
Determine the response of the system to the input signal
x(n)={1,1,2,3}
?
(c) Determine the inverse z-transform of the function 07
X(Z) = , |Z| >1
OR
Q.3 (a) Find Z-transform of x(n) = [2(4)
n
? 4(2)
n
] u(n) 03
(b) State and prove the differentiation property of Z transform. 04
(c) Determine the response of the system, 07
y(n) = y(n-1) - y(n-2) + x(n) to the input
signals. x(n) = ?(n) - ? (n-1)
Q.4 (a) Define DFT. 03
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2170914 Date: 15/11/2018
Subject Name: Digital Signal Processing
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) A discrete ?time signal x(n) is given below :
X(n) = {1,2,1,-2,1,2,3,4,14}
?
Sketch and label carefully each of the following signals:
(i) x(n-2) (ii) x(-4-n) (iii) x(n/2)
(b) List advantages of Digital Signal Processing over Analog
Signal Processing.
(c) Find the linear convolution of following pairs of discrete
sequences
(i) x
1
(n) = {1,2,3,4,12,4,6} h
1
(n) = {4,3,2,1}
(ii) x
1
(n) = {1,2,1,2,1,2,1} h
1
(n) = {1,2,3,4,3,2,1}
MARKS
03
04
07
Q.2 (a) Obtain Fourier transform of single sided exponential pulse 03
x(n) = a
n
u(n)
(b) Check the following systems for time invariance and 04
Linearity : (i) y(n) = n[x(n)]
2
(ii) y(n) = a[x(n)]
2
+b x(n)
(c) Calculate DTFT of following signals 07
(i) x(n) = [ ? ,?, ?, ? ] (ii) x(n) = 2( ? )
n
u(n)
OR
(c) Explain Inverse system, minimum phase system and all pass 07
system. Determine Inverse of the system characterized by
y(n)=0.5y(n-1)+x(n) assuming zero initial conditions.
Q.3
(a)
Find the Z Transform of u(n-1)
03
(b) The impulse response of the LTI system is h(n)={2,4,5,6}. 04
?
Determine the response of the system to the input signal
x(n)={1,1,2,3}
?
(c) Determine the inverse z-transform of the function 07
X(Z) = , |Z| >1
OR
Q.3 (a) Find Z-transform of x(n) = [2(4)
n
? 4(2)
n
] u(n) 03
(b) State and prove the differentiation property of Z transform. 04
(c) Determine the response of the system, 07
y(n) = y(n-1) - y(n-2) + x(n) to the input
signals. x(n) = ?(n) - ? (n-1)
Q.4 (a) Define DFT. 03
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(b) Find the IDFT of Y(K)={1,0,1,0} 04
(c) Explain 8-point DFT from two 4 point DFTs using radix-2 07
Decimation in frequency (DIF) FFT algorithm.
OR
Q.4 (a) Find the Circular convolution of following pairs of discrete 03
sequences
(i) x
1
(n) = {3,2,3,4} x
2
(n) ={ 1,3,1,3,2,1}
? ?
(b) Obtain the value of X(4) for 8 point DFT if 04
x(n) = {1,-1,0,2,1,-2,-1,1}
(c) Derive DIT FFT flow graph for N = 4 hence find DFT of 07
x(n) = {1, 2, 3, 4}
Q.5 (a) Write a note on windowing. 03
(b) Determine H(Z) by using impulse invariant method if H(s) = 04
and sampling time is 0.01 sec.
(c) Obtain Direct Form I & II realization of a system described 07
by
y(n) ? 1/6 y(n ? 1) + 1/3 y(n-2) = x(n) + 2x(n-2)
OR
Q.5 (a) Compare Decimation in Time and Decimation in Frequency. 03
(b) Explain Floating point Digital signal processors.
04
(c) With the help of a neat sketch, explain Digital Signal
07
Processor architecture.
**********
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This post was last modified on 20 February 2020