Test: The Z-Transform


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20 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: The Z-Transform

Test: The Z-Transform for Railways 2022 is part of GATE Electrical Engineering (EE) 2023 Mock Test Series preparation. The Test: The Z-Transform questions and answers have been prepared according to the Railways exam syllabus.The Test: The Z-Transform MCQs are made for Railways 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: The Z-Transform below.
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Test: The Z-Transform - Question 1

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

Test: The Z-Transform - Question 2

X(z) = ln(1 + z-1), |z| > 0

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

Test: The Z-Transform - Question 3

If z-transform is given by

X(z) = cos(z-3), |z| > 0

The value of x[12] is

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

Test: The Z-Transform - Question 4

X(z) of a system is specified by a pole zero pattern in fig.

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

All gives the same z transform with different ROC. So all are the solution.

Test: The Z-Transform - Question 5

Consider three different signal

fig.shows the three different region. Choose the correct option for the ROC of signal

R1  , R2 , R3

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

x1[n] is right-sided signal

Test: The Z-Transform - Question 6

Given

For three different ROC consider there different solution of signal x[n] :

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

Test: The Z-Transform - Question 7

X(z) has poles at z =1/2 and z =-1.If x [1] = 1 x [-1] = 1, and the ROC includes the point z = 34. The time signal x[n] is

Detailed Solution for Test: The Z-Transform - Question 7

Since the ROC includes the z = 3/4, ROC is

Test: The Z-Transform - Question 8

x[n] is right-sided, X (z) has a signal pole, and x[0] = 2, x[2] = 1/2. x[n] is

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

Test: The Z-Transform - Question 9

The z-transform function of a stable system is given as

The impuse response h[n] is

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

h[n] is stable, so ROC includes |z| = 1

Test: The Z-Transform - Question 10

Let x[n] = δ[n-2] + δ[n+2]  The unilateral z-transform is

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

Test: The Z-Transform - Question 11

The unilateral z-transform of signal x[n] = u[ n + 4 ] is

Detailed Solution for Test: The Z-Transform - Question 11

Test: The Z-Transform - Question 12

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: The Z-Transform - Question 12

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

Test: The Z-Transform - Question 13

The transfer function of a system is given as

The h[n] is

Detailed Solution for Test: The Z-Transform - Question 13

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

Test: The Z-Transform - Question 14

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: The Z-Transform - Question 14

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

Test: The Z-Transform - Question 15

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: The Z-Transform - Question 15

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: The Z-Transform - Question 16

The system

is stable if

Detailed Solution for Test: The Z-Transform - Question 16

Test: The Z-Transform - Question 17

Consider the following three systems

The equivalent system are

Detailed Solution for Test: The Z-Transform - Question 17

So y1 and y2 are equivalent.

Test: The Z-Transform - Question 18

The z-transform of a causal system is given as

The x[0] is

Detailed Solution for Test: The Z-Transform - Question 18

Test: The Z-Transform - Question 19

The z-transform of a anti causal system is

The value of x[0] is

Detailed Solution for Test: The Z-Transform - Question 19

Test: The Z-Transform - Question 20

Given the z-transforms

The limit of x[ ∞] is

Detailed Solution for Test: The Z-Transform - Question 20

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

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