Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 7th Sem New 2171708 Digital Signal Processing Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VII (New) EXAMINATION ? WINTER 2019
Subject Code: 2171708 Date: 26/11/2019
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) How Digital signal processing is better than Analog signal processing? Explain
in brief.
03
(b) A discrete time signal is given by
x(n)= { 2, 1, 1, 2, 1 }
?
sketch the following signal:
(1) x (n+1) (2) x (n ? 2)
(2) x (n) u (n-1) (4) x (n - 1) ? (n -1)
04
(c) A Digital communication link carries binary coded words representing samples
of an input signal
x a(t) = 3 cos600? t + 2 cos1800? t
The link is operated at 10000 bits/sec and each input sample is quantized into
1024 different voltage level.
(a) What is the sampling frequency & folding frequency?
(b) What is the Nyquist rate for the signal x a (t)?
(c) What are the frequencies in the resulting discrete time signal x (n)?
(d) What is the resolution ??
07
Q.2 (a) Determine the autocorrelation of the sequence
x (n) ={1,5,1,2}
?
03
(b) Obtain the linear convolution of
x (n) = {1,2,2,1} h(n) = {1,2,1}
04
(c) Determine the response of the system
y (n) =5/6 y (n-1) - 1/6 y(n-2) + x(n) to the input signal
x (n) = ?(n)
07
OR
(c) Prove that LTI system is stable if its impulse response is absolutely summable.
Test the stability of a system where impulse is
h (n) = a
n
u(n).
07
Q.3 (a) Prove that LTI system is causal if its impulse response
h (n)= 0 for n < 0
03
(b) Determine if the following discrete time systems are
(1) Causal or non causal
(2) Linear or non linear
(a) y(n) = cos x(n)
(b) y(n) =x(n
2
)
04
(c) Determine the inverse Z transform of the following using partial fraction
expansion method.
X(z) = z
3
/(z-1)(z-1/2)
2
|z| ? 1
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VII (New) EXAMINATION ? WINTER 2019
Subject Code: 2171708 Date: 26/11/2019
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) How Digital signal processing is better than Analog signal processing? Explain
in brief.
03
(b) A discrete time signal is given by
x(n)= { 2, 1, 1, 2, 1 }
?
sketch the following signal:
(1) x (n+1) (2) x (n ? 2)
(2) x (n) u (n-1) (4) x (n - 1) ? (n -1)
04
(c) A Digital communication link carries binary coded words representing samples
of an input signal
x a(t) = 3 cos600? t + 2 cos1800? t
The link is operated at 10000 bits/sec and each input sample is quantized into
1024 different voltage level.
(a) What is the sampling frequency & folding frequency?
(b) What is the Nyquist rate for the signal x a (t)?
(c) What are the frequencies in the resulting discrete time signal x (n)?
(d) What is the resolution ??
07
Q.2 (a) Determine the autocorrelation of the sequence
x (n) ={1,5,1,2}
?
03
(b) Obtain the linear convolution of
x (n) = {1,2,2,1} h(n) = {1,2,1}
04
(c) Determine the response of the system
y (n) =5/6 y (n-1) - 1/6 y(n-2) + x(n) to the input signal
x (n) = ?(n)
07
OR
(c) Prove that LTI system is stable if its impulse response is absolutely summable.
Test the stability of a system where impulse is
h (n) = a
n
u(n).
07
Q.3 (a) Prove that LTI system is causal if its impulse response
h (n)= 0 for n < 0
03
(b) Determine if the following discrete time systems are
(1) Causal or non causal
(2) Linear or non linear
(a) y(n) = cos x(n)
(b) y(n) =x(n
2
)
04
(c) Determine the inverse Z transform of the following using partial fraction
expansion method.
X(z) = z
3
/(z-1)(z-1/2)
2
|z| ? 1
07
2
OR
Q.3 (a) Find the Z transform and sketch ROC of
x (n)= a
n
u(n) + ? (n-3)
03
(b) State & prove differentiation property of Z transform. 04
(c) Find the inverse Z transform of the following using long division method.
(1) X(z)= z / z-1 |z| ? 1
(2) X(z)= z / z-a if |z| ? |a|
07
Q.4 (a) Describe the relationship between DFT & Z- transform. 03
(b) Explain linearity & periodicity properties of DFT. 04
(c) The transfer function of a causal LTI system is
H(z)= (1-z
-1
) / (1+3/4 z
-1
)
(1) Find the impulse response of the system.
(2) Find the output of the system to the input
x (n) = (1/3)
n
u(n) + u (-n-1)
(3) Is the system stable?
07
OR
Q.4 (a) Compute the DFT of the following:
(1) x (n) = ? (n)
(2) x (n) = ? (n ? n0)
03
(b) Find the circular convolution of the following sequences:
x (n) = {1,2,3,4} h(n) ={2,1,1,2}
04
(c) Consider the LTI system initially at rest, described by the difference equation,
y (n) =1/4 y (n-2) + x(n)
(1) determine h(n) of the system
(2) Determine direct form ?II, parallel form & cascade form realization of this
system.
07
Q.5 (a) Explain frequency Aliasing. 03
(b) Write the properties of
(a) humming window
(b) hanning window
04
(c) Explain bilinear transformation method of designing IIR filter. 07
OR
Q.5 (a) Find inverse DFT of X(K) ={1,2,3,4} 03
(b) The transfer function of analog filter is
H(s) = 3 / (s+2) (s+3) with Ts= 0.1 sec
Design IIR filters using bilinear transformation.
04
(c) Explain Radix-2 decimation in frequency FFT algorithm. 07
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This post was last modified on 20 February 2020