1
POKHARA UNI VERSI TY
Level: Bachelor
Semester
–
Fall
Year : 2009
Programme:
B.E.
Full Marks : 100
Course:
Digital Signal Processing
Time : 3hrs.
Candidates are required to give their answers in their own words as far
as practicable.
The figures in the margin indicate full marks.
Attempt all the questions.
1.
a)
Why do we need to perform digital signal processing? Compare
digital signal processing with analog signal processing? What are the
limitations of digital signal processing? Di
scuss.
b)
Given the analog signal
;
12000
cos
10
6000
sin
5
2000
cos
3
)
(
t
t
t
t
X
a
find the
following:
i.
What is the Nyquist rate for this signal?
ii.
If this signal is sample
d
using sampling rate 5000
samples/sec; what is the discrete time signal obtained
after sampling?
iii.
What is the data
rate if each input sample is quantized
into 1024 different voltage levels?
iv.
What is the analog signal
)
(
t
y
a
that can be
reconstructed from samples if we use ideal interpolation?
7
8
2.
a)
A discrete time system can be
i.
Static or dynamic
ii.
Li
near or non linear
iii.
Time invariant or time varying
iv.
Causal or noncausal
v.
Stable or unstable
b)
What is convolution? Write steps to perform convolution of two
sequences (graphically).
c)
State and prove the necessary and sufficeint conditions for stability
of LTI sy
stems.
5
5
5
3
a)
Define z

transform and Region of Convergence. Find z

transform of
following signal using properties.
]
[
]
[
n
u
na
n
x
n
, Also mention ROC of this signal
b)
The step response of a causal, stable LTI system is:
7
8
2
].
[
)
2
1
(
]
[
n
u
n
y
n
Where u [n] is the unit step function.
i.
Find the z

domain transfer function of this system.
ii.
Find the impulse response h [n] of this system.
iii.
Find the linear constant coefficient difference
(LCCD) equation that describes this system.
iv.
Plot magnitude resp
onse of this system
4.
a)
Find out the circular convolution of two sequences x1[n]&x2[n]
such that
x1[n]={1,2,3,4}
x2[n]={4,3,2,1}
b)
Given a sequence x
(
n
)
={0,1,2,3,4,5,6
,7
}, determine x[k] using
DIT FFT algorithm.
7
8
5.
a)
Determine the cascade and p
arallel realization
s
for the system
described by the system.
)
2
1
1
)(
4
3
1
(
)
3
1
3
4
1
(
)
(
2
1
1
1
1
z
z
z
z
z
z
H
b)
Draw the lattice structure for the following IIR system
)
8
.
1
4
.
1
2
1
)
(
2
1
z
z
z
H
7
8
6.
a)
Explain how the windows are used to design FIR filters? Explain
wit
h examples of Rectangular and Kaiser windows.
b)
Explain symmetrical and asymmetrical FIR filters.
8
7
7.
Write short notes on
(Any Two):
a)
Gibb's Phenomenon
b)
Bit serial arithmetic implementation of DSP processor
c)
Recursive and nom

recursive system.
5x2
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