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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 y_{1} and y_{2} 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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