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.

20 on this page

SubjectTopicYearType

The impedance parameters

Z_{11}

Z_{12}

of the two-port network in the figure are

An ideal sawtooth voltage waveform of frequency

500 \mathrm{~Hz}

3 \mathrm{~V}

is generated by charging a capacitor of

2 \; \mu \mathrm{F}

in every cycle. The charging requires

\mathrm{P}

\mathrm{Q}

be time-invariance,

\mathrm{R}

be causality and

\mathrm{S}

be stability. A discrete-time system has the input-output relationship,

y(n)=\left\{\begin{array}{ll} x(n) & n \geq 1 \\ 0, & n=0 \\ x(n+1), & n \leq-1 \end{array}\right.

x(n)

is the input and

y(n)

is the output. …

Data for Q. 63-64 are given below. Solve the problems and choose the correct answers. The system under consideration is an RC low-pass filter (RC-LPF) with

R=1.0 \mathrm{k} \; \Omega \mathrm{k}

\mathrm{C}=1.0 \; \mu \mathrm{F}

\mathrm{H}(f)

denote the frequency response of the RC-LPF. Let

f_{1}

be the highest frequency such that …

Data for Q. 63-64 are given below. Solve the problems and choose the correct answers. The system under consideration is an

R C

low-pass filter (RC-LPF) with

R=1.0 \; \mathrm{k} \Omega \mathrm{k}

\mathrm{C}=1.0 \; \mu \mathrm{F}

t_{g}(f)

be the group delay function of the given RC-LPF and

f_{2}=100 \mathrm{~Hz}

x(t)=2 \cos (800 \pi t)+\cos (1400 \pi t) . x(t)

is sampled with the rectangular pulse train shown in the figure. The only spectral components (in

\mathrm{kHz}

) present in the sampled signal in the frequency range

2.5 \; \mathrm{kHz}

3.5 \; \mathrm{kHz}

Consider a sampled signal

y(t)=5 \times 10^{\circ}

{ }^6 x(t) \sum_{(n-\infty}^{+\infty} \delta \left(t-n \mathrm{T}_x\right)

x(t)=10 \cos \left(8 \pi \times 10^3\right) t

T_s=100 \; \mu \mathrm{sec}

y(t)

is passed through an ideal lowpass filter with a cut-off frequency of 5

\mathrm{kHz}

, the output of the filter is

A linear phase channel with phase delay

T_p

and group delay

T_g

f

denotes frequency)

The Fourier transform

\mathrm{F}\left\{e^{-t} u(t)\right\}

\frac{1}{1+j 2 \pi f}

\mathrm{F}\left\{\frac{1}{1+j 2 \pi t}\right\}

Which of the following cannot be the Fourier series expansion of a periodic signal ?

x(t+5)

with impulse function

\delta(t-7)

In given figure

1.2,

the switch was closed for a long time before opening at

t=0

V x

t=0^{+}

The dependent current source shown in given figure.

If the variance

\sigma_{x}^{2}

d(n)=x(n)-x(n-1)

is one-tenth the variance

\sigma_{x}^{2}

of a stationary zero-mean discrete-time signal

x(n)

, then the normalized autocorrelation function

R_{x x}(k) / \sigma_{x}^{2}

k=1

x(t)=100 \cos \left(24 \pi \times 10^{3}\right) t

is ideally sampled with a sampling period of

50 \; \mu \mathrm{sec}

and then passed through an ideal lowpass filter with cut-off frequency of

15 \; \mathrm{kHz}

. Which of the following frequencies is/are present at the filter output?

m(t)=\frac{2 \sin 2 \pi t}{t}, s(t)=\cos 200 \pi t

n(t)

=\frac{\sin 199 \pi t}{t}

y(t)

If the impulse response of a discrete-time system is

h[n]=-5^{n} u[-n-1]

, then the system function

\mathrm{H}(z)

The Laplace transform of a continuous-time signal

x(t)

X(s)=\frac{5-s}{s^{2}-s-2}

. If the Fourier transform of this signal exists, then

x(t)

3

-phase balanced source in the figure is delivers

1500 \mathrm{~W}

at a leading power factor of

0.844

, then the value of

Z_{L}

(in ohm) is approximately

In the network of the figure is the maximum power is delivered to

R_{\mathrm{L}}

if its value is