How To Exam?

a knowledge trading engine...

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

Wednesday, 16 January 2013 05:50Web

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

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:

***********************

( 0 Votes )

#### Add comment

Refresh

 Earning:   Approval pending.
You are here: