Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 7th Sem Old 171003 Digital Signal Processing Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (OLD) EXAMINATION ? WINTER 2018
Subject Code: 171003 Date: 26/11/2018
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 defined as
?? (?? ) = {
1 +
?? 3
? 3 ? ?? ? 1
1 0 ? n ? 3
0 ?????????? ???????
a) Determine its value and Sketch the signal.
b) Sketch the signal if
I. First fold ?? (?? )and then delay the resulting signal by four samples
II. First delay ?? (?? ) by four samples and then fold the resulting signal
c) Compare above results. Is folding and Delay Operation is commutative
operation?
d) Can you express the signal ?? (?? ) in terms of ?? (?? ) and ?? (?? ) ?
07
(b) For each of following system determine whether system is stable, causal,
Linear, Time invariant or not.
1. ?? (?? ) = ? ?? (?? )
?? +1
?? =??
2. ?? (?? ) = ?? (?? 2
)
3. ?? (?? ) = ???????? (?? )
07
Q.2 (a) Prove that convergence of absolute sum of the impulse response is a sufficient
condition for BIBO (bounded input bounded output) stability of LTI system.
07
(b) Obtain a linear convolution of following two discrete-time signals:
?? (?? ) = ? ?? (?? ? ?? )
2
?? =0
?(?? ) = 2
?? [?? (?? ) ? ?? (?? ? 3)]
07
OR
(b) Enlist Properties of linear convolution.
Obtain linear Convolution for ?? (?? ) = { 1,1,0,1,1} and ?(?? ) = { 1, ?2, ?3,4}
07
Q.3 (a) What is ROC? Explain the properties of ROC in Z-Transform. 07
(b) Find magnitude Response and Phase Response of system described by
differential equation
?? (?? ) ?
1
2
?? (?? ? 1) = ?? (?? ) ?
1
4
?? (?? ? 1)
07
OR
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (OLD) EXAMINATION ? WINTER 2018
Subject Code: 171003 Date: 26/11/2018
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 defined as
?? (?? ) = {
1 +
?? 3
? 3 ? ?? ? 1
1 0 ? n ? 3
0 ?????????? ???????
a) Determine its value and Sketch the signal.
b) Sketch the signal if
I. First fold ?? (?? )and then delay the resulting signal by four samples
II. First delay ?? (?? ) by four samples and then fold the resulting signal
c) Compare above results. Is folding and Delay Operation is commutative
operation?
d) Can you express the signal ?? (?? ) in terms of ?? (?? ) and ?? (?? ) ?
07
(b) For each of following system determine whether system is stable, causal,
Linear, Time invariant or not.
1. ?? (?? ) = ? ?? (?? )
?? +1
?? =??
2. ?? (?? ) = ?? (?? 2
)
3. ?? (?? ) = ???????? (?? )
07
Q.2 (a) Prove that convergence of absolute sum of the impulse response is a sufficient
condition for BIBO (bounded input bounded output) stability of LTI system.
07
(b) Obtain a linear convolution of following two discrete-time signals:
?? (?? ) = ? ?? (?? ? ?? )
2
?? =0
?(?? ) = 2
?? [?? (?? ) ? ?? (?? ? 3)]
07
OR
(b) Enlist Properties of linear convolution.
Obtain linear Convolution for ?? (?? ) = { 1,1,0,1,1} and ?(?? ) = { 1, ?2, ?3,4}
07
Q.3 (a) What is ROC? Explain the properties of ROC in Z-Transform. 07
(b) Find magnitude Response and Phase Response of system described by
differential equation
?? (?? ) ?
1
2
?? (?? ? 1) = ?? (?? ) ?
1
4
?? (?? ? 1)
07
OR
2
Q.3 (a) What is canonic and non-canonic structure? Obtain Direct form-I and Direct form
II realization of the following transfer function.
?? (?? ) =
3 + 3.6?? ?1
+ 0.6?? ?2
1 + 0.1?? ?1
? 0.2?? ?2
07
(b) Prove differentiation property of Z-transform and obtain the Z-transform of
nu(n) using the same.
07
Q.4 (a) The system function of the analog filter is given as
?? ?? =
?? + 0.1
(?? + 0.1)
2
+ 9
Obtain the system function of the IIR digital filter by using impulse invariance
method.
07
(b) State and Prove following Properties in terms of DFT.
1. Time Reversal
2. Periodicity
07
OR
Q.4 (a) Compare FIR and IIR filters. 07
(b) Determine the response of FIR filter using DFT if
?? (?? ) = { 1,2} and ?(?? ) = { 2,2}
07
Q.5 (a) Explain Decimation in Time FFT algorithm. 07
(b) Derive the DFT of the sample data sequence ?? (?? ) = { 1,1,2,2,3,3} determine the
corresponding amplitude and phase spectrum.
07
OR
Q.5 (a) Explain multiplier-Accumulator (MAC) hardware in DSP processors. 07
(b) Discuss the applications of digital signal processing with suitable examples. 07
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This post was last modified on 20 February 2020