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

A stable linear time variant (LTI) system has a transfer function

H(s) = \frac{1}{s^2+s-6}

. To make this system casual it needs to be cascaded with another LTI system having a transfer function

H_1(s)

. A correct choice for

H_1(s)

among the following options is

A casual LTI system has zero initial conditions and impulse response

h(t)

x(t)

y(t)

are related through the linear constant-coefficient differential equation

\frac{d^2y(t)}{dt^2} + a \frac{dy(t)}{dt}+a^2y(t)=x(t).

Let another signal

g(t)

g(t)=a^2 \int_0^t h(\tau) d \tau +\frac{dh(t)}{dt}+ah(t).

N

X

x[n]

0 \leq n \leq N-1

X[k] = \frac{1}{\sqrt{N}} \Sigma_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N}nk}, \: \: \: 0 \leq k \leq N-1.

Denote this relation as

X=DFT(x)

N=4

, which one of the following sequences satisfies

DFT(DFT(x))=x

Consider a transfer function

G_p(s) = \frac{ps^2+3ps-2}{s^2+(3+p)s+(2-p)}

p

a positive real parameter. The maximum value of

p

G_p

remains stable is ___________.

The characteristic equation of a unity negative feedback system is

1+KG(s)=0

. The open loop transfer function

G(s)

has one pole at

0

and two poles at

-1

. The root locus of the system for varying

K

is shown in the figure. The constant damping ratio line, for

\xi = 0.5

, intersects the root locus at point A. The distance from the origin …

Two systems with impulse responses

h_{1}(t)

h_{2}(t)

are connected in cascade. Then the overall impulse response of the cascaded system is given by

The impulse response of a system is

h(t) = tu(t).

u(t − 1),

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor

k, \: k> 0,

the elements of the corresponding star equivalent will be scaled by a factor of

For a periodic signal

v(t) = 30\sin100\:t + 10\cos300\:t + 6\sin(500\:t+\pi/4),

the fundamental frequency in

rad/s

A band-limited signal with a maximum frequency of

5\: kHz

is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

The transfer function

\dfrac{V_{2}(s)}{V_{1}(s)}

of the circuit shown below is

g(t) = e^{-\pi t^{2}},

h(t)

is a filter matched to

g(t).

g(t)

is applied as input to

h(t),

then the Fourier transformation of the output is

In the circuit shown below, if the source voltage

V_S = 100\angle 53.13^{\circ}\: V

then the Thevenin’s equivalent voltage in Volts as seen by the load resistance

R_{L}

The open-loop transfer function of a dc motor is given as

\dfrac{\omega(s)}{V_{a}(s)} = \dfrac{10}{1+10s}.

When connected in feedback as shown below, the approximate value of

K_{a}

that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

The impulse response of a continuous time system is given by

h(t) = \delta(t-1) + \delta(t-3).

The value of the step response at

t = 2

The state diagram of a system is shown below. A system is described by the state-variable equations

\dot{X}= AX+Bu;\:\: y = CX+Du

The state-variable equations of the system shown in the figure above are

The unilateral Laplace transform of

f(t)

\frac{1}{s^2+s+1}

. The unilateral Laplace transform of

tf(t)

A system with transfer function

G(s)=\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}

\sin(\omega t)

. The steady-state output of the system is zero at

In the circuit shown below, the current through the inductor is