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

The block diagram of a system is illustrated in the figure shown, where

X(s)

is the input and

Y(s)

is the output. The transfer function

H(s)=\dfrac{Y(s)}{X(s)}

Let the state-space representation of an LTI system be

x(t)=A x(t)+B u(t), y(t)=Cx(t)+du(t)

A,B,C

d

u(t)

is the input to the system, and

y(t)

is its output. Let

B=[0\quad0\quad1]^{T}

d=0

.Which one of the following options for

A

C

will ensure that the transfer function of this LTI …

Consider a unity feedback system, as in the figure shown, with an integral compensator

\dfrac{K}{s}

and open-loop transfer function

G(s)=\dfrac{1}{s^{2}+3s+2}

K>0.

The positive value of

K

for which there are exactly two poles of the unity feedback system on the

j\omega

axis is equal to ________ (rounded off to two decimal …

h[n]

be a length –

7

discrete-time finite impulse response filter, given by

h[0]=4, \quad h[1]=3,\quad h[2]=2,\quad h[3]=1,

\quad h[-1]=-3, \quad h[-2]=-2, \quad h[-3]=-1,

h[n]

|n|\geq4.

3

finite impulse response approximation

g[n]

h[n]

has to be obtained such that …

A discrete-time all-pass system has two of its poles at

0.25\angle 0^{\circ}

2\angle 30^{\circ}

. Which one of the following statements about the system is TRUE?

\text{x(t)}

be a periodic function with period

\text{T = 10}

.The Fourier series coefficients for this series are denoted by

a_{k},

x\left ( t \right )=\sum ^{\infty }_{k=-\infty }a_{k}e^{jk\:\frac{2\pi }{T}t}

The same function

x(t)

can also be considered as a periodic function with period

{T}'=40.

b_{k}

\text{ABCD}

matrix for a two-port network is defined by:

\begin{bmatrix} V_{1}\\ I_{1} \end{bmatrix}=\begin{bmatrix} A &B \\ C& D \end{bmatrix}\begin{bmatrix} V_{2}\\ -I_{2} \end{bmatrix}

\text{B}

for the given two-port network (in ohms, correct to two decimal places) is _________.

The state equation and the output equation of a control system are given below:

\dot{x}=\begin{bmatrix} -4 & -1.5\\ 4& 0 \end{bmatrix}x+\begin{bmatrix} 2\\ 0 \end{bmatrix}u,

y=\begin{bmatrix} 1.5 & 0.625 \end{bmatrix}x.

The transfer function representation of the system is

4\sin c(2t)

is fed to a Hilbert transformer to obtain

y( t),

as shown in the figure below: Here

\sin c \left ( x\right )=\dfrac{\sin\left ( \pi x \right )}{\pi x}.

The value (accurate to two decimal places) of

\int ^{\infty }_{-\infty } \mid y( t ) \mid ^{2}dt

For a unity feedback control system with the forward path transfer function

G\left ( s \right )=\dfrac{K}{s\left ( s+2 \right )}

The peak resonant magnitude

M_{r}

of the closed-loop frequency response is

2

. The corresponding value of the gain

\text{K}

(correct to two decimal places) is _________.

The figure below shows the Bode magnitude and phase plots of a stable transfer function

G\left ( s \right )=\dfrac{n_{0}}{s^{3}+d_{2}s^{2}+d_{1}s+d_{0}}.

Consider the negative unity feedback configuration with gain

k

in the feedforward path. The closed loop is stable for

k < k_{0}.

The maximum value of

k_{0}

Consider the network shown below with

R_{1}=1\:\Omega,R_{2}=2\:\Omega

R_{3}=3\:\Omega.

The network is connected to a constant voltage source of

11\:V

. The magnitude of the current (in amperes, accurate to two decimal places ) through the source is _________.

A band limited low-pass signal

x(t)

5\:kHz

is sampled at a sampling rate

f_{s}

x(t)

is reconstructed using the reconstruction filter

H(f)

whose magnitude response is shown below: The minimum sampling rate

f_{s}(\text{in}\: kHz)

for perfect reconstruction of

x(t)

X\left[ k \right ] = k + 1,0\leq k\leq 7

8

\:\text{DFT}\:

x[n]

X\left [ k \right ]=\sum_{n=0}^{N-1}x \left [ n \right ]e^{-j2\pi nk/N}

. The value (correct to two decimal places) of

\sum_{n=0}^{3}x \left [ 2n \right ]

Consider the following statements for continuous-time linear time invariant (LTI) systems. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. There is no causal and BIBO stable with a pole in the right half of the complex plane. Which one among the following is correct?

Consider a single input single output discrete-time system with

x[ n ]

y [ n ]

as output, where the two are related as

y [ n ]= \begin{cases} n \mid x [ n ] \mid, & \text{ for } \ 0\leq n\leq 10\\ x [ n ] – x [ n-1 ], & \text{otherwise.}\end{cases}

Which one of the following statements is true about the system?

A periodic signal

x(t)

has a trigonometric Fourier series expansion

x( t )= a_{0}+\sum_{n=1}^{ \infty } ( a_{n} \cos n\omega _{0}t+b_{n}\sin n\omega _{0}t )

x(t)= -x(-t)=-x(t-\frac{\pi }{\omega _{0}})

, we can conclude that

x(t)

be a continuous time periodic signal with fundamental period

T=1

{a_{k} }

be the complex Fourier series coefficients of

x(t)

k

is integer valued. Consider the following statements about

x(3t)

: The complex Fourier series coefficients of

x(3t)

{a_{k}}

k

is integer valued The complex …

Two discrete-time signals

x[n]

h[n]

are both non-zero only for

n=0,1,2

, and are zero otherwise .It is given that

x[0]=1, \: x[1]=2, \: x[2]=1, \: h[0]=1

y[n]

be the linear convolution of

x[n]

h[n]

y[1]=3

y[2]=4

, the value of the expression

(10y[3]+y[4])

h[n]

be the impulse response of a discrete-time linear time invariant(LTI) filter. The impulse response is given by

h[0]=\frac{1}{3}; \, h[1]=\frac{1}{3}; \, h[2]=\frac{1}{3} \text{; and } h[n]=0 \text{ for } n<0 \text{ and } n>2.

H(\omega)

be the discrete-time Fourier transform (DTFT) of

h[n]

\omega

is the normalized …