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

In the network shown in the figure, all resistors are identical with

R = 300 \Omega

. The resistance

R_{ab}

\Omega

) of the network is __________.

The result of the convolution

x(-t) * \delta (-t-t_0)

The waveform of a periodic signal

x(t)

is shown in the figure. A signal

g(t)

g(t) = x \big( \frac{t-1}{2} \big)

. The average power of

g(t)

A sinusoidal signal of

2

kHz frequency is applied to a delta modulator. The sampling rate and step-size

\Delta

of the data modulator are

20,000

samples per second and

0.1

V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is

Consider the signal

s(t)=m(t) \cos(2 \pi \: f_ct)+ \hat{m}(t) \sin(2 \pi f_c t)

\hat{m}(t)

denotes the Hilbert transform of

m(t)

and the bandwidth of

m(t)

is very small compared to

f_c

s(t)

The damping ratio of a series RLC circuit can be expressed as

In the circuit shown, switch SW is closed at

t=0

. Assuming zero initial conditions, the value of

v_c(t)

t=1

sec is _________.

In the given circuit, the maximum power (in Watts) that can be transferred to the load

R_L

For the discrete-time system shown in the figure, the poles of the system transfer function are located at

The pole-zero diagram of a casual and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity

4

. The impulse response of the system is

h[n]

h[0]=1

, we can conclude

The open-loop transfer function of a plant in a unity feedback configuration is given as

G(s) = \frac{K(s+4)}{(s+8)(s^2-9)}

. The value of the gain

K(>0)

-1+j2

lies on the root locus is _________.

A lead compensator network includes a parallel combination of

R

C

in the feed-forward path. If the transfer function of the compensator is

G_c(s)=\frac{s+2}{s+4}

RC

is ___________.

A plant transfer function is given as

G(s)= \bigg( K_p+ \frac{K_1}{s} \bigg) \frac{1}{s(s+2)}

. When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is

In the system shown in Figure (a),

m(t)

is a low-pass signal with bandwidth

W

Hz. The frequency response of the band-pass filter

H(f)

is shown in Figure (b). If it is desired that the output signal

z(t)=10x(t)

, the maximum value of

W

(in Hz) should be strictly less than _____________.

The bilateral Laplace transform of a function

f(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\ 0 & \text{otherwise} \end{cases}

The magnitude and phase of the complex Fourier series coefficients ܽ

a_{k}

of a periodic signal

x(t)

are shown in the figure. Choose the correct statement from the four choices given. Notation:

C

is the set of complex numbers, ܴ

R

is the set of purely real numbers, and

P

ܲis the set of purely imaginary numbers.

(ܸV_{C})

across the capacitor (in Volts) in the network shown is ______.

In the circuit shown, the average value of the voltage

V_{ab}

(in Volts) in steady state condition is ________.

Let the signal ݂

f(t) = 0

outside the interval

[T_{1},T_{2}]

T_{1}

T_{2}

are finite. Furthermore,

\mid f(t) \mid < \infty

. The region of convergence (RoC) of the signal’s bilateral Laplace transform

F(s)

Two causal discrete-time signals

x[n]

y[n]

y[n] = \displaystyle{}\sum _{m=0}^{n} x[m]

z

y[n]

\dfrac{2}{z(z-1)^{2}},

x[2]