GATE ECE 2015 Set 3 | Miscellaneous Question 3 | Signals and Systems

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

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

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

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

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

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 2007

MCQ (Single Correct Answer)

-0.6

A Hilbert transformer is a

non-linear system

non-causal system

time-varying system

low-pass system

GATE ECE 2007

MCQ (Single Correct Answer)

-0.6

In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be: GATE ECE 2007 Signals and Systems - Miscellaneous Question 4 English 1