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

1 \; \mathrm{kHz}

sinusoidal signal is ideally sampled at

1500

samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequencey

800 \mathrm{~Hz}

. The output signal has the frequency

A rectangular pulse train

s(t)

as shown in the figure is convolved with the signal

\cos ^{2}\left(4 p \times 10^{3} t\right)

. The convolved signal will be a

\text{LTI}

system is described by the difference equation

2 y[n]=\alpha y[n-2]-2 x[n]+\beta x[n-1]

The system is stable only if

The impulse response

h|n|

of a linear time invariant system is given as

h[n]=\left\{\begin{array}{cc} -2 \sqrt{2} & n=1,-1 \\ 4 \sqrt{2} & n=2,-2 \\ 0, & \text{ otherwise } \end{array}\right.

If the input to the above system is the sequence

\mathrm{e}^{j \pi n / 4}

, then the output is

x(t)

y(t)

(with Fourier transforms

X(f)

Y(f)

respectively) be related as shown in the given figure. Then

Y(f)

Consider the signal

x(t)

shown in the figure. Let

h(t)

denote the impulse response of the filter matched to

x(t)

h(t)

being non-zero only in the interval 0 to

4 \; \mathrm{sec}

h(t)

in the interval

3 < t < \text{sec}.

Consider a system shown in the figure. Let

X(f)

Y(f)

denote the Fourier transforms of

X(t)

y(t)

respectively. The ideal HPF has the cutoff frequency

10 \mathrm{kHz}

. The positive frequencies where

Y(f)

has spectral peaks are

Consider an impedance

\mathrm{Z = R + j X }

marked with point

\mathrm{P}

in an impedance Smith chart as shown in the figure. The movement from point

\mathrm{P}

along a constant resistance circle in the clockwise direction by an angle

45^{\circ}

is equivalent to

The minimum number of equations required to analyze the circuit shown in the figure is

A source of angular frequency

1 \; \mathrm{rad} / \mathrm{sec}

has a source impedance consisting of

1 \Omega

resistance in series with

1 \; \mathrm{H}

inductance. The load that will obtain the maximum power transfer is

\text{RLC}

circuit has a resonance frequency of

1 \; \mathrm{kHz}

and a quality factor

\text{Q}=100

\text{R, L}

\text{C}

is doubled from its original value, the new

\text{Q}

of the circuit is

The differential equation for the current

i(t)

in the circuit of the figure is

The Fourier series expansion of a real periodic signal with fundamental frequency

\mathrm{f}_0

g_p(t)=\sum_{n=-\infty}^{\infty} c_n e^{j 2 \pi n f_\omega t}

It is given that

c_3=3+j 5

c_{-3}

x(t)

be the input to a linear, time-invariant system. The required output is

4 x(t-2)

. The transfer function of the system should be

x(n)

with the z-transform

X(z)=z^4+z^2-2 z+2-3 z-4

is applied as an input to a linear, time-invariant system with the impulse response

h(n)=2 \delta(n-3)

\delta(n)= \begin{cases}1, & n=0 \\ 0, & \text{ otherwise }\end{cases}

n=4

1 \; \Omega

resistance are used as edges to form a cube. The resistance between two diagonally opposite corners of the cube is

The circuit for

\text{Q. 33-34}

are given in the figure. For both are the questions, assume that the switch

S

1

for a long time and thrown to position

2

t=0

t=0+

i_{1}

The circuit for

\text{Q. 33-34}

are given in the figure. For both are the questions, assume that the switch

S

1

for a long time and thrown to position

2

t=0

I_{1}(s)

I_{2}(s)

are the Laplace transforms of

i_{1}(t)

i_{2}(t)

respectively. The equations for the loop currents

I_{1}(s)

An input voltage

v(t)=10 \sqrt{2} \cos \left(t+10^{\circ}\right)+10 \sqrt{3}

\cos \left(2 t+10^{\circ}\right) \mathrm{V}

is applied to a series combination of resistance

R=1 \Omega

and an inductance

L=1H

. The resulting steady-state current

i(t)

The driving-point impedance

Z(s)

of a network has the pole-zero locations as shown in the figure. If

Z(0)=3

Z(s)