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Biju Patnaik University of Technology BPUT
**Course:
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B.Tech
**Specialization:
**Electronics and Instrumentation Engineering**Offline Downloads:
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Total Number of Pages : 02
B.Tech.
PCEC4304
6th Semester Back Examination 2017-18
DIGITAL SIGNAL PROCESSING
BRANCH : AEIE, CSE, ECE, EEE, EIE, ETC, IEE, MECH
Time : 3 Hours
Max Marks : 70
Q.CODE : C334
Answer Question No.1 which is compulsory and any five from the rest.
The figures in the right hand margin indicate marks.
Q1
a)
b)
Determine the values of power and energy signal of x (n) u ( n) .
c)
Represent the sequence x(n) 4,2,1, 1, 3, 2,1, 5 as sum of shifted unit
impulses.
State the difference between DIT and DIF filter.
Find the Z-transform of the signal x (n) sin( n ) u ( n) .
d)
e)
f)
g)
h)
i)
j)
Q2
a)
b)
Q3
Q4
(2 x 10)
Answer the following questions :
Write the major applications of DSP telemetry.
1
3
n
What is zero padding? What are it’s used?
What is twiddle factor? What are its properties?
How many multiplications and additions are required to compute 32-point
DFT using radix-2 FFT?
What is wrapping?
How one can design digital filters from analog filters?
Show that the following systems are nonlinear and time invariant.
y(n) – x(n)y(n-1) = x(n)
1
1 Z 1
4
Using Residue Method, find inverse Z-transform of X ( Z )
,
1 2
1 Z
4
1
ROC: Z
.
3
(5)
(5)
a)
Find the natural response of the system described by difference equation
with
initial
conditions
y (n) 2 y( n 1) y (n 2) x(n) x( n 1)
y (1) y ( 2) 1 .
(6)
b)
Distinguish between recursive realization and non-recursive realization.
(4)
a)
b)
Find the DFT of a sequence x(n) ={1 ,1, 3,4,4,3,2,1}
Find the Z-transform of x(n)= (1/8)n u(n) and its ROC.
(5)
(5)

Q5
a)
b)
Obtain the direct form I, direct form II and Cascade form realization of the
following system functions.
Y(n) = 0.1 y(n-1) + 0.2 y(n-2) + 3x(n) + 3.6 x(n-1) + 0.6 x(n-2).
Using impulse invariance method, with T=1sec determine H(z) if
H (s)
Q6
(a)
(6)
(4)
1
s2 2 s 1
The linear convolution of a length 50 sequence with the length of 500
sequences is to be computed using 64-point DFTs and IDFTs.
i) What is the smallest numbers of DFTs and IDFTs needed to compute
the linear convolution using over-lap add method?
ii) What is the smallest numbers of DFTs and IDFTs needed to compute
the linear convolution using over-lap save method?
(b) The system function of the analog filter is given as H a ( s )
( S 0.1)
.
( S 0.1) 2 9
(5)
(5)
Obtain the system function of the IIR digital filter by using Impulse Invariance
Method.
Q7
Perform
the
circular
convolution
of
the
following
sequences
(10)
x( n) 1,1, 2,1 and h(n) 1, 2, 3, 4 using DFT and IDFT Method.
Q8
a)
b)
c)
d)
Write short answer on any TWO :
Section Convolution
DIF FFT
ROC of Z-transform
DCT is an orthogonal transform
(5 x 2)

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