GATE ECE 2009 | GATE ECE Year Wise Previous Years Questions

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

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence $$\left\{ {1,\,0,\,2,\,3} \right\}$$ is

$$\left[ {0,\, - 2 + 2j,\,2,\, - 2 - 2j} \right]$$

$$\left[ {2,\,2 + 2j,\,6,\,2\, - 2j} \right]$$

$$\left[ {6,\,1 - 3j,\,2,\,1 + 3j} \right]$$

$$\left[ {6,\, - 1 + 3j,\,0,\, - 1\, - 3j} \right]$$

GATE ECE 2009

MCQ (Single Correct Answer)

-0.3

A function is given by f(t) = sin²t +cos2t . Which of the following is true?

f has frequency components at 0 and $$1/2\mathrm\pi$$ Hz

f has frequency components at 0 and $$1/\mathrm\pi$$ Hz

f has frequency components at $$1/2\mathrm\pi$$ and $$1/\mathrm\pi$$ Hz

f has frequency components at 0, $$1/2\mathrm\pi$$ and $$1/\mathrm\pi$$ Hz

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