Test: The Z-Transform

Question 1

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Accepted Answer

Answer

Answer

Answer

Question 2

X(z) = ln(1 + z^-1), |z| > 0

Accepted Answer

Answer

Answer

Answer

Question 3

If z-transform is given by

X(z) = cos(z^-3), |z| > 0

The value of x[12] is

Accepted Answer

1/24

Answer

-1/24

Answer

-1/6

Answer

1/6

Question 4

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

Accepted Answer

All three

Answer

x1[n]

Answer

x2[n]&#160;

Answer

x3[n]

Question 5

Consider three different signal

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

R₁ , R₂ , R₃

Accepted Answer

x₁[n], x₃[n], x₂[n]

Answer

x₁[n], x₂[n], x₃[n]

Answer

x₂[n], x₃[n], x₁[n]

Answer

x₃[n], x₂[n], x₁[n]

Question 6

Given

For three different ROC consider there different solution of signal x[n], (casual approch)

Accepted Answer

a and c

Answer

a and b

Answer

b and c

Answer

a, b, c

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

Accepted Answer

Answer

Answer

Answer

Question 8

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

Accepted Answer

Answer

Answer

Answer

Question 9

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

The impuse response h[n] is

Accepted Answer

Answer

Answer

Answer

Question 10

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

Accepted Answer

z-2

Answer

z2

Answer

-2 z-2

Answer

2 z2

Question 11

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

Accepted Answer

1/1-z-1

Answer

1 + z + z² + 3z + z⁴

Answer

1/1-z

Answer

1 + z^-1 + z^-2+ z^-3 + z^-4

Question 12

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

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

Accepted Answer

Answer

Answer

Answer

Question 13

The transfer function of a system is given as

The h[n] is

Accepted Answer

Stable and Causal

Answer

Stable

Answer

Causal

Answer

None of the above

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

Accepted Answer

Both (i) and (ii) are true

Answer

(i) is true

Answer

(ii) is true

Answer

Both are false

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

Accepted Answer

(i) is true

Answer

(ii) is true

Answer

Both are true

Answer

Both are false

Question 16

The system

is stable if

Accepted Answer

|c| &#60; 1.12

Answer

c&#160;&#60; 1.12

Answer

c&#160;&#62; 1.12

Answer

|c| &#62; 1.12

Question 17

Consider the following three systems

The equivalent system are

Accepted Answer

y₁[n] and y₂[n]

Answer

y₂[n] and y₃[n]

Answer

y₃[n] and y₁[n]

Answer

all

Question 18

The z-transform of a causal system is given as

The x[0] is

Accepted Answer

2

Answer

-1.5

Answer

1.5

Answer

0

Question 19

The z-transform of a anti causal system is

The value of x[0] is

Accepted Answer

4

Answer

-7/4

Answer

0

Answer

Does not exist

Question 20

Given the z-transforms

The limit of x[ ∞] is

Accepted Answer

1

Answer

2

Answer

&#8734;

Answer

0

GATE Electrical Engineering (EE) Test: The Z-Transform Free Online Test

MCQ Practice Test & Solutions: Test: The Z-Transform (20 Questions)

X(z) = ln(1 + z^-1), |z| > 0

If z-transform is given by
X(z) = cos(z^-3), |z| > 0
The value of x[12] is

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

Consider three different signal
fig.shows the three different region. Choose the correct option for the ROC of signal
R₁ , R₂ , R₃

Given
For three different ROC consider there different solution of signal x[n], (casual approch)

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

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

The z-transform function of a stable system is given as
The impuse response h[n] is

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

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

The z-transform of a signal x[n] is given by
If X (z) converges on the unit circle, x[n] is

The transfer function of a system is given as
The h[n] is

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

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

The system
is stable if

Consider the following three systems
The equivalent system are

The z-transform of a causal system is given as
The x[0] is

The z-transform of a anti causal system is
The value of x[0] is

Given the z-transforms
The limit of x[ ∞] is

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GATE Electrical Engineering (EE) Test: The Z-Transform Free Online Test

MCQ Practice Test & Solutions: Test: The Z-Transform (20 Questions)

​ ​ ​

X(z) = ln(1 + z-1), |z| > 0

If z-transform is given byX(z) = cos(z-3), |z| > 0The value of x[12] is

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

Consider three different signalfig.shows the three different region. Choose the correct option for the ROC of signalR1 , R2 , R3

GivenFor three different ROC consider there different solution of signal x[n], (casual approch)

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

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

The z-transform function of a stable system is given asThe impuse response h[n] is

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

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

The z-transform of a signal x[n] is given byIf X (z) converges on the unit circle, x[n] is

The transfer function of a system is given asThe h[n] is

The transfer function of a system is given asConsider the two statementsStatement(i) : System is causal and stable. Statement(ii) : Inverse system is causal and stable.The correct option is

The impulse response of a system is given byFor this system two statement areStatement (i): System is causal and stableStatement (ii): Inverse system is causal and stable.The correct option is

The systemis stable if

Consider the following three systemsThe equivalent system are

The z-transform of a causal system is given asThe x[0] is

The z-transform of a anti causal system isThe value of x[0] is

Given the z-transformsThe limit of x[ ∞] is

GATE Electrical Engineering (EE) Mock Test Series 2027

GATE Electrical Engineering (EE) Mock Test Series 2027

Top Courses for Electrical Engineering (EE)

About this Electrical Engineering (EE) Practice Test

Explore more Electrical Engineering (EE) Study Resources

X(z) = ln(1 + z^-1), |z| > 0

If z-transform is given by
X(z) = cos(z^-3), |z| > 0
The value of x[12] is

Consider three different signal
fig.shows the three different region. Choose the correct option for the ROC of signal
R₁ , R₂ , R₃

Given
For three different ROC consider there different solution of signal x[n], (casual approch)

The z-transform function of a stable system is given as
The impuse response h[n] is

The z-transform of a signal x[n] is given by
If X (z) converges on the unit circle, x[n] is

The transfer function of a system is given as
The h[n] is

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

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

The system
is stable if

Consider the following three systems
The equivalent system are

The z-transform of a causal system is given as
The x[0] is

The z-transform of a anti causal system is
The value of x[0] is

Given the z-transforms
The limit of x[ ∞] is