Anna University Coimbatore 2009 B.E 2 ks with Answers for TPDE (Unit-5 Z-Transforms) - 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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