Download GTU BE/B.Tech 2019 Summer 7th Sem Old 171003 Digital Signal Processing Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 7th Sem Old 171003 Digital Signal Processing Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?VII (OLD) EXAMINATION ? SUMMER 2019
Subject Code: 171003 Date: 16/05/2019

Subject Name:Digital Signal Processing

Time: 02:30 PM TO 05:00 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) Draw the block diagram architecture of TMSC6000 series Digital Signal
Processor. Briefly describe each block functions.
07
(b) Define ROC for z-transform? List the properties of the ROC. 07

Q.2 (a) State and prove Time Shifting and Scaling in z domain properties for z-
transform.
07
(b) State and prove convolution theorem and the correlation theorem for Fourier
transform
07
OR
(b) Determine the z-transform of the following signals.
i) ( ) ( ) x n u n ? (3-Marks)
ii)
0
( ) (cos ) (n) x n n u ? ? (4-Marks)
07

Q.3 (a)
Determine the inverse z-transform of
12
1
()
1 1.5 0.5
Xz
zz
??
?
??
if
(i) ROC: 1 z ?
(ii) ROC: 0.5 z ?
(iii)ROC: 0.5 1 z ??
07
(b) Determine the range of value of a and b for which the liner time-invariant system
with impulse response
,0
()
,0
n
n
an
hn
bn
? ?
?
?
?
?
?
?

is stable.
07
OR
Q.3 (a) Determine the spectra of the signals
i) ( ) cos 2 x n n ? ? (3-marks)
ii) ( ) cos / 3 x n n ? ? (4-marks)
07
(b) The impulse response of a linear time invariant system is
? ?
( ) 1,2,3,1 hn
?
?
Determine the response of the system to the input signal
? ?
( ) 1,2,1, 1 xn
?
??
07

Q.4 (a) Compute the DFT of the four-point sequence (n) {0 1 2 3} x ? 07
(b) Obtain direct form-I and direct form-II structures for the system
3 1 1
( ) ( 1) ( 2) x(n) ( 1)
4 8 3
y n y n y n x n ? ? ? ? ? ? ? .
07



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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?VII (OLD) EXAMINATION ? SUMMER 2019
Subject Code: 171003 Date: 16/05/2019

Subject Name:Digital Signal Processing

Time: 02:30 PM TO 05:00 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) Draw the block diagram architecture of TMSC6000 series Digital Signal
Processor. Briefly describe each block functions.
07
(b) Define ROC for z-transform? List the properties of the ROC. 07

Q.2 (a) State and prove Time Shifting and Scaling in z domain properties for z-
transform.
07
(b) State and prove convolution theorem and the correlation theorem for Fourier
transform
07
OR
(b) Determine the z-transform of the following signals.
i) ( ) ( ) x n u n ? (3-Marks)
ii)
0
( ) (cos ) (n) x n n u ? ? (4-Marks)
07

Q.3 (a)
Determine the inverse z-transform of
12
1
()
1 1.5 0.5
Xz
zz
??
?
??
if
(i) ROC: 1 z ?
(ii) ROC: 0.5 z ?
(iii)ROC: 0.5 1 z ??
07
(b) Determine the range of value of a and b for which the liner time-invariant system
with impulse response
,0
()
,0
n
n
an
hn
bn
? ?
?
?
?
?
?
?

is stable.
07
OR
Q.3 (a) Determine the spectra of the signals
i) ( ) cos 2 x n n ? ? (3-marks)
ii) ( ) cos / 3 x n n ? ? (4-marks)
07
(b) The impulse response of a linear time invariant system is
? ?
( ) 1,2,3,1 hn
?
?
Determine the response of the system to the input signal
? ?
( ) 1,2,1, 1 xn
?
??
07

Q.4 (a) Compute the DFT of the four-point sequence (n) {0 1 2 3} x ? 07
(b) Obtain direct form-I and direct form-II structures for the system
3 1 1
( ) ( 1) ( 2) x(n) ( 1)
4 8 3
y n y n y n x n ? ? ? ? ? ? ? .
07



2



OR
Q.4 (a) State the Sampling theorem. Consider the analog signal
(t) 3cos2000 t 5sin6000 t 10cos12000 t
a
x ? ? ? ? ? ? .
i) What is the Nyquist rate for this signal?
ii) Assume now that we sample this signal using a sampling rate
Fs=5000samples/s. What is the discrete-time signal obtained after
sampling?
07
(b) How many numbers of additions, multiplications and memory locations will be
required to realize a system H(z) having M zeros and N poles in (i) Direct-form
I and Direct-form-II realization?. (ii) Give direct form-I and Direct form-II
structures of second order system realization.
07

Q.5 (a) Perform the circular convolution of the following two sequences:
? ?
? ?
1
2
(n) 2,1,2,1
(n) 1,2,3,4
x
x
?
?
?
?

07
(b) Classify the discreate time signals. Give one example of each class. 07
OR

Q.5 (a) Differentiate IIR and FIR systems. 07
(b) Explain the Decimation in Time FFT algorithm. 07

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