GATE ECE 2009 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2009

MCQ (Single Correct Answer)

-0.3

The ROC of Z-transform of the discrete time sequence
x(n)= $${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over 2}} \right)^{ n}}\,u( - n - 1)$$ is

$${1 \over 3} < \left| {z\,} \right| < {1 \over 2}$$

$$\left| {z\,} \right| > {1 \over 2}$$

$$\left| {z\,} \right| < {1 \over 2}$$

$$2 < \left| {z\,} \right| < 3$$

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

Consider a system whose input x and output y are related by the equation $$$y(t) = \int\limits_{ - \infty }^\infty {x(t - \tau )\,h(2\tau )\,d\tau } $$$

Where h(t) is shown in the graph.

GATE ECE 2009 Signals and Systems - Continuous Time Linear Invariant System Question 15 English

Which of the following four properties are possessed by the system?

BIBO: Bounded input gives a bounded output.
Causal: The system is casual.
LP: The system is low pass.
LTI: The system is linear and time- invariant.

Causal, LP

BIBO, LTI

BIBO, Causal, LTI

LP, LTI

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

A system with transfer function H(z) has impulse response h(.) defined as h(2) = 1, h(3) = - 1 and h (k) = 0 otherwise. Consider the following statements.
S1: H(z) is a low-pass filter.
S2: H(z) is an FIR filter.

Which of the following is correct?

Only S2 is true

Both S1 and S2 are false.

Both S1 and S2 are true, and S2 is a reason for S1.

Both S1 and S2 are true, but S2 is not a reason for S1.

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

An LTI system having transfer function $${{{s^2} + 1} \over {{s^2} + 2s + 1}}$$ and input x(t) = sin (t + 1) is in steady state. The output is sampled at a rate $${\omega _s}\,\,rad/s$$ to obtain the final output {y(k)}. Which of the following is true?

y(.) is zero for all sampling frequencies $${\omega _s}$$

y(.) is nonzero for all sampling frequencies $${\omega _s}$$

y(.) is nonzero for $${\omega _s}$$ > 2, but zero for $${\omega _s}$$ < 2

y(.) is zero for $${\omega _s}$$ > 2, but nonzero for $${\omega _s}$$ < 2

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2023