Anna University Coimbatore 2009 B.E 2 ks with Answers for TPDE %28Unit-5 Z-Transforms%29 - Question Paper
TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS
POSSIBLE TWO MARKS QUESTIONS WITH ANSWERS
UNIT -V
Z-TRANSFORM
TWO MARKS
1)
Find 
in
Z-transform.
Solution:
.
2)
Find 
using
Z-transform.
Solution:
.
3) State and prove initial value theorem in Z-transform.
Solution:
Statement:
If 
then
.
Proof:
4)
Find the
Z-transform of 
Solution:
5)
Find the
Z-transform of 
Solution:
.
6) State the final value theorem in Z-transform.
Solution:
Statement:
If 
then
.
Proof: Refer Text Book
7)
Find 
.
Solution:
8)
Evaluate 
.
Solution:
Consider,
Put
in
,
Similarly,
Put 
in
,
.
9)
Prove that 
.
Solution:
.
10)
Prove that 
.
Solution:
W.K.T.,
.
Here 
.
11)
Prove that 
.
Solution:
or
.
12)
Find 
.
Solution:
13)
Find the initial
and final values of the function 
.
Solution:
By Initial Value Theorem, 
.
By Final Value Theorem, 
.
14)
Find the
Z-transform of i) 
ii)
iii)
iv)
.
Solution:
i) 
.
The ROC is 
.
ii) 
.
The ROC is 
.
iii) 
W.K.T.,
Here
,
Therefore, 
iv) 
.
.
15)
What is the
Z-transform of 
.
Solution:
16) State the convolution property of Z-transform.
Solution:
i)
Where 
ii) 
Where 
.
17) State and prove shifting theorem of Z-transform.
Solution:
Statement:
First Shifting Theorem,
If 
then
.
Second Shifting Theorem,
If 
then
.
Proof: Refer text book
18)
Find the
Z-transform of 
.
Solution:
19)
Find the
Z-transform of 
Solution:
W.K.T., 
(By
Linearity Property )
20)
Prove that 
.
Solution:
21)
Find the
Z-transform of 
.
Solution:
22)
Prove that 
Solution:
23)
Find the
difference equation from 
Solution:
24)
Find 
.
Solution:
.
25) Define unit impulse sequence and find its Z-transform.
Solution:
A discrete unit impulse function is defined by 
.
Therefore, 
26) Define convolution of two sequences.
Solution:
27)
Find the
inverse Z-transform of 
Solution:
W.K.T.,
.
Here 
,
28)
From the
difference equation of 
,find
in
terms of 
.
Solution:
Taking Z-Transform on both sides
.
29)
Find 
,where
for
n= 0, 1, 2, .
Solution:
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| Earning: Approval pending. |
