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Test: Z-Transform - 3 - Electronics and Communication Engineering (ECE) MCQ


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10 Questions MCQ Test Signals and Systems - Test: Z-Transform - 3

Test: Z-Transform - 3 for Electronics and Communication Engineering (ECE) 2024 is part of Signals and Systems preparation. The Test: Z-Transform - 3 questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Z-Transform - 3 MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Z-Transform - 3 below.
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Test: Z-Transform - 3 - Question 1

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

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

Detailed Solution for Test: Z-Transform - 3 - Question 1


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

Test: Z-Transform - 3 - Question 2

The transfer function of a system is given as

The h[n] is

Detailed Solution for Test: Z-Transform - 3 - Question 2

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

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Test: Z-Transform - 3 - 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

Detailed Solution for Test: Z-Transform - 3 - Question 3

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.

Test: Z-Transform - 3 - 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

Detailed Solution for Test: Z-Transform - 3 - Question 4



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.

Test: Z-Transform - 3 - Question 5

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

Detailed Solution for Test: Z-Transform - 3 - Question 5

Test: Z-Transform - 3 - Question 6

Consider the following three systems


The equivalent system are

Detailed Solution for Test: Z-Transform - 3 - Question 6



So y1 and y2 are equivalent.

Test: Z-Transform - 3 - Question 7

The z-transform of a causal system is given as

The x[0] is

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Causal signal 

Test: Z-Transform - 3 - Question 8

The z-transform of a anti causal system is

The value of x[0] is

Detailed Solution for Test: Z-Transform - 3 - Question 8

Anti causal signal, 

Test: Z-Transform - 3 - Question 9

Given the z-transforms

The limit of x[∝] is

Detailed Solution for Test: Z-Transform - 3 - Question 9

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

Test: Z-Transform - 3 - Question 10

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

Detailed Solution for Test: Z-Transform - 3 - Question 10



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