Test: Z-Transform Part - 3


10 Questions MCQ Test Signal and System | Test: Z-Transform Part - 3


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This mock test of Test: Z-Transform Part - 3 for Electrical Engineering (EE) helps you for every Electrical Engineering (EE) entrance exam. This contains 10 Multiple Choice Questions for Electrical Engineering (EE) Test: Z-Transform Part - 3 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Z-Transform Part - 3 quiz give you a good mix of easy questions and tough questions. Electrical Engineering (EE) students definitely take this Test: Z-Transform Part - 3 exercise for a better result in the exam. You can find other Test: Z-Transform Part - 3 extra questions, long questions & short questions for Electrical Engineering (EE) on EduRev as well by searching above.
QUESTION: 1

The z-transform of a signal x[n] is given by

If X (z) converges on the unit circle, x[n] is

Solution:


Since X (z) converges on |z|= 1. So ROC must include this circle.

QUESTION: 2

The transfer function of a system is given as

The h[n] is

Solution:

 So system is both stable and causal. ROC includes z = 1.

QUESTION: 3

The transfer function of a system is given as

Consider the two statements
Statement(i) : System is causal and stable.
Statement(ii) : Inverse system is causal and stable.
The correct option is

Solution:

Pole of system at :
Pole of inverse system at : 
For this system and inverse system all poles are inside |z|= 1. So both system are both causal and stable.

QUESTION: 4

The impulse response of a system is given by

For this system two statement are
Statement (i): System is causal and stable
Statement (ii): Inverse system is causal and stable.
The correct option is

Solution:



Pole of this system are inside |z|= 1. So the system is stable and causal.
For the inverse system not all pole are inside |z|= 1.So inverse system is not stable and causal.

QUESTION: 5

The system
y[n] = cy[n - 1] -0.12 y[n - 2 ] + x[n - 1] + x[n - 2 ] is stable if

Solution:

QUESTION: 6

Consider the following three systems


The equivalent system are

Solution:



So y1 and y2 are equivalent.

QUESTION: 7

The z-transform of a causal system is given as

The x[0] is

Solution:

Causal signal 

QUESTION: 8

The z-transform of a anti causal system is

The value of x[0] is

Solution:

Anti causal signal, 

QUESTION: 9

Given the z-transforms

The limit of x[∝] is

Solution:

The function has poles at z = 1, 3/4. Thus final value theorem applies.

QUESTION: 10

The impulse response of the system shown in fig. P5.4.62 is

Solution:



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