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 circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output

V_{o}

( rounded off to two decimal places) is ______

V

The loop transfer function of a negative feedback system is

G\left ( s \right )H\left ( s \right )=\frac{K(s+11)}{s(s+2)(s+8)}.

K

, for which the system is marginally stable, is ___________.

I

in the given network is

A finite duration discrete-time signal

x[n]

is obtained by sampling the continuous-time signal

x\left ( t \right )=\cos\left ( 200\pi t \right )

at sampling instants

t=n/400, n=0, 1, \dots ,7.

8

-point discrete Fourier transform

\text{(DFT)}

x[n]

is defined as …

For the given circuit, which one of the following is correct state equation?

Using the incremental low frequency small-signal model of the

\text{MOS}

device, the Norton equivalent resistance of the following circuit is

A system with transfer function

G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+a \right )},\:\:a> 0

is subjected to an input

5 \cos3t

. The steady state output of the system is

\dfrac{1}{\sqrt{10}}\cos\left ( 3t-1.892 \right )

a

X\left ( \omega \right )

is the Fourier transform of

x(t)

shown below. The value of

\int_{-\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega

(rounded off to two decimal places) is ____________

The transfer function of a stable discrete-time

\text{LTI}

H\left ( z \right )=\dfrac{K\left ( z-\alpha \right )}{z+0.5}

K

\alpha

are real numbers. The value of

\alpha

(rounded off to one decimal place) with

\mid \alpha \mid > 1

, for which the magnitude response of the system is constant over all frequencies, …

Consider the following closed loop control system where

G\left ( s \right )=\dfrac{1}{s\left ( s+1 \right )}

C\left ( s \right )=K\dfrac{s+1}{s+3}

. If the steady state error for a unit ramp input is

0.1

, then the value of

K

is ______________.

H(z)

z-

transform of a real-valued discrete-time signal

h[n].

P(z) = H(z) H(\frac{1}{z})

z= \frac{1}{2}+\frac{1}{2}j,

P(z)

has a total of four zeros, which one of the following plots represents all the zeros correctly?

Consider the two-port resistive network shown in the figure. When an excitation of

5\: V

is applied across Port

1

2

is shorted, the current through the short circuit at Port

2

is measured to be

1\: A

(see (a) in the figure). Now, if an excitation of

5\: V

is applied across Port

2

1

is shorted (see (b) in …

Y(s)

be the unit-step response of a causal system having a transfer function

G(s)= \dfrac{3-s}{(s+1)(s+3)}

Y(s)=\dfrac{G(s)}{s}.

The forced response of the system is

For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles

N_{p}

and the number of system zeros

N_{z}

in the frequency range

1\: Hz \leq f \leq \:10^{7} Hz

Consider the signal

f(t)=1+2 \cos(\pi t)+3 \sin \left(\dfrac{2\pi}{3}t\right)+4 \cos \left(\dfrac{\pi}{2}t+\dfrac{\pi}{4}\right)

t

is in seconds. Its fundamental time period, in seconds, is __________.

The baseband signal

m(t)

shown in the figure is phase-modulated to generate the

PM

\varphi(t)=\cos(2\pi f_{c}t+ k\:\: m(t)).

t

x-

axis in the figure is in milliseconds. If the carrier frequency is

f_{c}=50\:kHz

k=10 \pi,

then the ratio of the minimum instantaneous frequency (in kHz) to the maximum …

In the circuit shown, the clock frequency, i.e., the frequency of the ClK signal, is

12\:kHz

. The frequency of the signal at

Q_{2}

is _______ kHz.

Consider a six-point decimation-in-time Fast Fourier Transform

(FFT)

algorithm, for which the signal-flow graph corresponding to

X[1]

is shown in the figure. Let

W_{6}=exp\left(-\:\dfrac{j2\pi}{6}\right).

In the figure, what should be the values of the coefficients

a_{1},a_{2},a_{3}

W_{6}

X[1]

is obtained …

In the circuit shown, if

v(t)=2 \sin(1000\: t)

R=1\:k \Omega

C=1\:\mu F,

then the steady-state current

i(t)

, milliamperes (mA), is

Consider a causal second-order system with the transfer function

G(s)=\dfrac{1}{1+2s+s^{2}}

with a unit-step

R(s)=\dfrac{1}{s}

as an input. Let

C(s)

be the corresponding output. The time taken by the system output

c(t)

94\%

of its steady-state value

\underset{t\rightarrow \infty}{\lim}\:c(t),

rounded off to two decimal …