GATE ECE 2002 | Discrete Time Linear Time Invariant Systems Question 20 | Signals and Systems

If the impulse response of a discrete-time system is $$h\left[ n \right]\, = \, - {5^n}\,\,u\left[ { - n\, - 1} \right],$$ then the system function $$H\left( z \right)\,\,\,$$ is equal to

$${{ - z} \over {z - 5}}$$ and the system is stable.

$${z \over {z - 5}}$$ and the system is stable.

$${{ - z} \over {z - 5}}$$ and the system is unstable.

$${z \over {z - 5}}$$ and the system is unstable.

GATE ECE 1992

MCQ (Single Correct Answer)

-0.6

A linear discrete - time system has the characteristic equation, $${z^3} - 0.81\,\,z = 0.$$ The system

is stable.

is marginally stable.

is unstable.

stability cannot be assessed from the given information.

GATE ECE 1988

MCQ (Single Correct Answer)

-0.6

Consider the system shown in the Fig.1 below. The transfer function $$Y\left( z \right)/X\left( z \right)$$ of the system is GATE ECE 1988 Signals and Systems - Discrete Time Linear Time Invariant Systems Question 20 English

GATE ECE 1988 Signals and Systems - Discrete Time Linear Time Invariant Systems Question 20 English

$${{1 + a\,{z^{ - 1}}} \over {1 + b\,{z^{ - 1}}}}$$

$${{1 + b\,{z^{ - 1}}} \over {1 + a\,{z^{ - 1}}}}$$

$${{1 + a\,{z^{ - 1}}} \over {1 - b\,{z^{ - 1}}}}$$

$${{1 - b\,{z^{ - 1}}} \over {1 + a\,{z^{ - 1}}}}$$

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Signals and Systems

Network Theory

Control Systems

Digital Circuits

General Aptitude

Electronic Devices and VLSI

Analog Circuits

Engineering Mathematics

Microprocessors

Communications

Electromagnetics