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

Consider a continuous-time finite-energy signal

f(t)

whose Fourier transform vanishes outside the frequency interval

\left[-\omega_{c}, \omega_{c}\right]

\omega_{c}

\mathrm{rad}

\mathrm{sec}

f(t)

is uniformly sampled to obtain

y(t)=f(t) \: p(t)

In the circuit below,

M_{1}

is an ideal AC voltmeter and

M_{2}

is an ideal AC ammeter. The source voltage (in Volts) is

v_{s}(t)=100 \cos (200 t)

. What should be the value of the variable capacitor

C

such that the RMS readings on

M_{1}

M_{2}

25 \: \mathrm{V}

5 \: \mathrm{A}

, respectively?

Z

-parameter matrix of a two port network relates the port voltages and port currents as follows:

\left[\begin{array}{l} V_{1} \\ V_{2} \end{array}\right]=Z\left[\begin{array}{l} I_{1} \\ I_{2} \end{array}\right]

Z

-parameter matrix (with each entry in Ohms) of the network shown below is

\_\_\_\_\_\_\_

f(t)

be a periodic signal with fundamental period

T_{0}>0

. Consider the signal

y(t)=f(\alpha t)

\alpha>1

. The Fourier series expansions of

f(t)

y(t)

are given by …

Two resistors are connected in a circuit loop of area

5 \mathrm{~m}^{2}

, as shown in the figure below. The circuit loop is placed on the

x-y

plane. When a time-varying magnetic flux, with flux-density

B(t)=0.5 t

(in Tesla), is applied along the positive

z

-axis, the magnitude of current

I

(in Amperes, rounded off to two decimal places) in …

A causal and stable

\text{LTI}

system with impulse response

h(t)

produces an output

y(t)

for an input signal

x(t)

x(0.5 t)

is applied to another causal and stable

\text{LTI}

system with impulse response

h(0.5 t)

. The resulting output is

\_\_\_\_\_\_\_

For a causal discrete-time LTI system with transfer function

H(z)=\frac{2 z^{2}+3}{\left(z+\frac{1}{3}\right)\left(z-\frac{1}{3}\right)}

which of the following statements is/are true?

In the circuit given below, the switch

\text{S}

was kept open for a sufficiently long time and is closed at time

t=0

. The time constant (in seconds) of the circuit for

t>0

\_\_\_\_\_\_

Consider two continuous time signals

x(t)

y(t)

as shown below If

X(f)

denotes the Fourier transform of

x(t)

, then the Fourier transform of

y(t)

\_\_\_\_\_\_

A continuous time signal

x(t)=2 \cos (8 \pi t+\pi / 3)

is sampled at a rate of

15 \mathrm{~Hz}

. The sampled signal

x_{s}(t)

when passed through an LTI system with impulse response

h(t)=\left(\frac{\sin 2 \pi t}{\pi t}\right) \cos (38 \pi t-\pi / 2)

produces an output

x_{o}(t)

. The expression for

x_{o}(t)

\_\_\_\_\_

The radian frequency value(s) for which the discrete time sinusoidal signal

x[n]=A \cos (\Omega n+\pi / 3)

has a period of

40

\_\_\_\_\_\_

The relationship between any N-length sequence

x[n]

and its corresponding

\mathrm{N}

-point discrete Fourier transform

X[k]

X[k]=\mathcal{F}\{x[n]\} .

Another sequence

y[n]

is formed as below

y[n]=\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{x[n]\}\}\}\} .

For the sequence

x[n]=\{1,2,1,3\}

, the value of …

For the two port network shown below, the value of the

Y_{21}

parameter (in Siemens) is

\_\_\_\_\_\_

In the network shown below, maximum power is to be transferred to the load

R_{L}

R_{L}

\Omega

\_\_\_\_\_\_\_

\text{RLC}

circuit has a quality factor

\text{Q}

1000

at a center frequency of

10^{6} \; \mathrm{rad} / \mathrm{s}

. The possible values of

\text{R, L}

\text{C}

Consider a system with input

x(t)

y(t)=x\left(e^{t}\right)

. The system is

m(t)

be a strictly band-limited signal with bandwidth

B

E

\omega_{0}=10 B

, the energy in the

m(t) \cos \omega_{0} t

The Fourier transform

X(\omega)

x(t)=e^{-t^{2}}

\int_{-\infty}^{\infty} e^{-y^{2}} d y=\sqrt{\pi}

In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic (a) Continuous, aperiodic (ii) Continuous, periodic (b) Continuous, periodic (iii) Discrete, aperiodic (c) Discrete, aperiodic (iv) Discrete, periodic (d) Discrete, periodic

For a real signal, which of the following is/are valid power spectral density/densities?