GATE ECE 2015 Set 3 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2015 Set 3

MCQ (Single Correct Answer)

-0.6

A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input x[n ] , the response y[ n] is GATE ECE 2015 Set 3 Signals and Systems - Discrete Time Signal Z Transform Question 18 English

GATE ECE 2015 Set 3 Signals and Systems - Discrete Time Signal Z Transform Question 18 English

$$4{\left( { - {1 \over 3}} \right)^n}u\left[ n \right] - 5{\left( { - {2 \over 3}} \right)^n}u\left[ n \right]$$

$$5{\left( { - {2 \over 3}} \right)^n}u\left[ n \right] - 3{\left( { - {1 \over 3}} \right)^n}u\left[ n \right]$$

$$5{\left( {{1 \over 3}} \right)^n}u\left[ n \right] - 5{\left( {{2 \over 3}} \right)^n}u\left[ n \right]$$

$$5{\left( {{2 \over 3}} \right)^n}u\left[ n \right] - 5{\left( {{1 \over 3}} \right)^n}u\left[ n \right]$$

GATE ECE 2015 Set 3

MCQ (Single Correct Answer)

-0.6

Suppose x $$\left[ n \right]$$ is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at z = ± 2j. Which one of the following statements is TRUE for the signal x=$$\left[ n \right]$$ ?

It is a finite duration signal.

It is a causal signal.

It is a non-causal signal.

It is a periodic signal.

GATE ECE 2015 Set 3

MCQ (Single Correct Answer)

-0.3

The impulse response of an LTI system can be obtained by

differentiating the unit ramp response

differentiating the unit step response

integrating the unit ramp response

integrating the unit step response

GATE ECE 2015 Set 3

MCQ (Single Correct Answer)

-0.6

The complex envelope of the bandpass signal $$x(t)\, = \, - \sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right)\sin \left( {\pi t - {\pi \over 4}} \right),$$ centered about f = $${1 \over {2\,}}\,Hz,$$ is

$$\left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{j{\pi \over 4}}}$$

$$\left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{ - j{\pi \over 4}}}$$

$$\sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{j{\pi \over 4}}}$$

$$\sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right){e^{ - j{\pi \over 4}}}$$

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