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

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

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

R_{1} , R_{2} , R_{3}

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

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

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

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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

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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

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

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Test: The Z-Transform - Question 17

Consider the following three systems

The equivalent system are

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

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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

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

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