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 figure shows an RLC circuit excited by the sinusoidal voltage

100 \cos(3t)

t

is in seconds. The ratio

\frac{\text{amplitude of }V_{2}}{\text{amplitude of }V{1}}

A continuous time signal

x(t)=4 \cos(200\pi t)+8 \cos(400\pi t)

t

is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response

h(t)=\begin{cases} \frac{2 \sin (300\pi t)}{\pi t},& t\neq 0 \\ 600, & t=0. \end{cases}

y(t)

be the output of this filter. The maximum value of

\mid y(t) \mid

In the circuit shown, V is a sinusoidal voltage source. The current

I

is in phase with voltage V. The ratio

\frac{\text{amplitude of voltage across the capacitor}}{\text{amplitude of voltage across the resistor}}

is ___________.

A connection is made consisting of resistance A in series with a parallel combination of resistances

B

C

. Three resistors of value

10 Ω, 5 Ω, 2 Ω

are provided. Consider all possible permutations of the given resistors into the positions

A, B, C

, and identify the configurations with maximum possible overall resistance, and also the ones …

An LTI system with unit sample response

h[n]=5\delta [n]-7\delta [n-1]+7\delta [n-3]-5\delta [n-4]

x(t)

y(t)

of a continuous –time system are related as

y(t)=\int_{t-T}^{t}x(u) du.

Consider the state space realization

\begin{bmatrix} \dot{x_1}(t)\\ \dot{x_2}(t) \end{bmatrix}=\begin{bmatrix} 0 &0 \\ 0&-9 \end{bmatrix}\begin{bmatrix} x_1(t)\\ x_2(t) \end{bmatrix}+\begin{bmatrix} 0\\ 45 \end{bmatrix} u(t)

, with the initial condition

\begin{bmatrix} x_1(0)\\ x_2(0) \end{bmatrix}=\begin{bmatrix} 0\\ 0 \end{bmatrix}

Consider the circuit shown in the figure. The Thevenin equivalent resistance (in Ω) across P-Q is _____________

Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are

\begin{array} {} h_1(t)=2\delta (t+2)-3\delta (t+1) \\ h_2(t)=\delta (t-2). \end{array}

x(t)

is a unit step signal, then the energy of

y(t)

is ____________

x(t)=\sin (14000\pi t)

t

is in seconds, is sampled at a rate of

9000

samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response

H(f)

H(f)=\begin{cases} 1, & \mid f \mid \leq 12 kHz .\\ 0,& \mid f \mid> 12 kHz. \end{cases}

What is the number of sinusoids …

Which one of the following is a property of the solutions to the Laplace equation:

\nabla^2f = 0

A continuous-time function

x(t)

is periodic with period

T

. The function is sampled uniformly with a sampling period

T_s

. In which one of the following cases is the sampled signal periodic?

Consider a two-port network with the transmission matrix:

T = \begin{pmatrix}A & B \\C & D\end{pmatrix}

. If the network is reciprocal, then

A continuous-time sinusoid of frequency

33 Hz

is multiplied with a periodic Dirac impulse train of frequency

46Hz

. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of

23Hz

. The fundamental frequency (in

Hz

) of the output is _______

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal

s(t) = 5 \cos1600 \pi t + 20 \cos 1800 \pi t + 5 \cos 2000 \pi t

. The value of the modulation index is _________

The Laplace transform of the casual periodic square wave of period

T

shown in the figure below is

A first-order low-pass filter of time constant

T

is excited with different input signals (with zero initial conditions up to

t = 0

). Match the excitation signals

X, Y, Z

with the corresponding time responses for

t \geq 0

Consider the signal

x[n] = 6 \delta[n + 2] + 3 \delta[n + 1] + 8 \delta[n] + 7 \delta[n - 1] + 4 \delta[n - 2]

X(e^{jw})

is the discrete-time Fourier transform of

x[n]

\frac{1}{\pi} \int\limits_{-\pi}^{\pi} X(e^{jw}) \sin^2(2\omega) d\omega

is equal to _______

The open-loop transfer function of a unity-feedback control system is

G(s)= \frac{K}{s^2+5s+5}

K

at the breakaway point of the feedback contol system’s root-locus plot is _________

The open-loop transfer function of a unity feedback control system is given by

G(s)= \frac{K}{s(s+2)}

. For the peak overshoot of the closed-loop system to a unit step input to be

10 \%

K