GATE EC Networks, Signals and Systems questions

Practise Networks, Signals and Systems questions for GATE EC. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

Identify whether the signal and system are continuous-time or discrete-time. Check linearity, time invariance and stability before selecting a transform or response method.

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SubjectTopicYearType

In the figure shown, assume that all the capacitors are initially uncharged. If

\text{V}_i(t)=10 u(t)

\text{V}_0(t)

m(t)

500 \mathrm{~Hz}

is first multiplied by a signal

g(t)

g(t)=\sum_{\mathrm{R}=-\infty}^{\infty}(-1)^{k} \delta\left(t-0.5 \times 10^{-4} k\right)

The resulting signal is then passed through an ideal lowpass filter with bandwidth

1 \; \mathrm{kHz}

. The output of the lowpass filter would be

The minimum sampling frequency (in samples/sec) required to reconstruct the following signal from its samples without distortion

x(t)=5\left(\frac{\sin 2 \pi 1000 t}{\pi t}\right)^{3}+7\left(\frac{\sin 2 \pi 1000 t}{\pi t}\right)^{2}

A system with input

x[n]

y[n]

y[n]=\left(\sin \frac{5}{6} \pi n\right) x(n)

. The system is

The minimum step-size required for a Delta-Modulator operating at

32 \mathrm{~K}

\mathrm{sec}

to track the signal (here

u(t)

is the unit-step function)

\begin{array}{l}x(t)=125 t(u(t)-u(t-1))+(250-125 t)(u(t-1) -u(t-2)) \end{array}

so that slope-overload is avoided, would be

In the following figure the minimum value of the constant '

C

', which is to be added to

y_{1}(t)

y_{1}(t)

y_{2}(t)

are different, is

Common Data for Questions 74, 75: Let

g(t)=p(t)^{*} p(t)

, where * denotes convolution and

p(t)=u(t)-u(t-1)

u(t)

being the unit step function The impulse response of filter matched to the signal

s(t)=g(t)-\delta(t-2)^{*} g(t)

Choose the function

f(t); – \infty < 1 < \infty,

for which a Fourier series cannot be defined.

x(t)

is shown in the figure. Even and odd parts of a unit-step function

u(t)

are respectively,

The region of convergence of

Z

-transform of the sequence

\left(\frac{5}{6}\right)^{n} u(n)-\left(\frac{6}{5}\right)^{n} u(-n-1)

The condition on

\mathrm{R}, \mathrm{L}

\mathrm{C}

such that the step response

y(t)

in the figure has no oscillations, is

\text{ABCD}

parameters of an ideal

n: 1

transformer shown in the figure are

\left[\begin{array}{ll}n & 0 \\ 0 & \mathrm{X}\end{array}\right]

X

\mathrm{RLC}

\mathrm{R}=2 \; \mathrm{k} \Omega, \mathrm{L}=1 \; \mathrm{H}

\mathrm{C} \frac{1}{400}=\mu \mathrm{F}

. The resonant frequency is

The maximum power that can be transferred to the load resistor

R_{L}

from the voltage source in the figure is

The first and the last critical frequency of an

\text{RC}

-driving point impedance function must respectively be

x(n)=\left(\frac{1}{2}\right)^{n} u(n), y(n)=x^{2}(n)

\mathrm{Y}\left(e^{j i e}\right)

be the Fourier transform of

y(n)

Y\left(e^{j i e}\right)

The power in the signal

s(t)=8 \cos \left(20 \pi t-\frac{\pi}{2}\right)+

4 \sin (15 \pi t)

In what range should

\operatorname{Re}(s)

remain so that the Laplace transform of the function

e^{(n+2)t+5}

For the circuit show in the figure, the instantaneous current

i_{i}(t)

\mathrm{Z}

as shown in the given figure is