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 Fourier transform of a signal

h(t)

H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega

h(0)

The state variable description of an LTI system is given by

\begin{pmatrix} \dot{x_1}\\ \dot{x_2}\\ \dot{x_3} \end{pmatrix}=\begin{pmatrix} 0 & a_1 & 0\\ 0 & 0 & a_2\\a_3 & 0 & 0 \end{pmatrix} \begin{pmatrix} x_1\\ x_2\\x_3 \end{pmatrix}+\begin{pmatrix} 0\\ 0\\1 \end{pmatrix}u

The circuit shown is a

y[n]

denote the convolution of

h[n]

g[n]

h[n]=(\frac{1}{2})^nu[n]

g[n]

is a casual sequence. If

y[0]=1

y[1]=\frac{1}{2}

g[1]

V_A-V_B=6\:V

V_C-V_D

10\:V

dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

1\: \Omega

connected at port B draws a current of

3\:A

2.5\: \Omega

connected at port B draws a current of

2\:A

10\: V

dc connected at port A, the current drawn by

7\:\Omega

connected at port B is

10\:V

dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

1\: \Omega

connected at port B draws a current of

3\:A

2.5\: \Omega

connected at port B draws a current of

2\:A

For the same network, with

6\: V

dc connected at port A,

1\:\Omega

connected at port B draws …

The transfer function of a compensator is given as

G_c(s)=\frac{s+a}{s+b}

G_c(s)

is a lead compensator if

The transfer function of a compensator is given as

G_c(s)=\frac{s+a}{s+b}

The phase of the above lead compensator is maximum at

Four messages band limited to

\text{W, W, 2W}

\text{3W}

respectively are to be multiplexed using

\text{Time Division Multiplexing (TDM)}.

The minimum bandwidth required for transmission of this

\text{TDM}

In delta modulation, the slope overload distortion can be reduced by

In the following scheme, if the spectrum

M(f)

m(t)

is as shown, then the spectrum

Y(f)

y(t)

A low-pass filter having a frequency response

\mathrm{H}(\mathrm{j} \omega)=\mathrm{A}(\omega) \;e^{j{\phi(\omega)}}

does not produce any phase distortion, if

x(t) \longleftrightarrow \mathrm{X}(j \omega)

be Fourier Transform pair. The Fourier Transform of the signal

x(5 t-3)

X(j \omega)

The Dirac delta function

\delta(t)

If the region of convergence of

x_1[n]+x_2[n]

\frac{1}{3}<|z|<\frac{2}{3}

, then the region of convergence of

x_1[n]-x_2[n]

A two-port network is represented by

\text{ABCD}

parameters given by

\left[\begin{array}{c} \mathrm{V}_1 \\ \mathrm{I}_1 \end{array}\right]=\left[\begin{array}{ll} \mathrm{A} & \mathrm{B} \\ \mathrm{C} & \mathrm{D} \end{array}\right]\left[\begin{array}{c} \mathrm{V}_2 \\ -\mathrm{I}_2 \end{array}\right]

2

is terminated by …

In the two port network shown in the figure below,

z_{12}

z_{21}

are, respectively

The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by

2 \; \mathrm{mH}

inductor with some initial current can be represented as shown below, where

s

is the Laplace Transform variable. The value of initial current is