ESE EE : Signals and Systems National Champion Test for ESE & GATE EE Exams

Question 1

The value of the integral

is

Question 2

The signal x(n) shown in the below figure is a

Question 3

The correlation function of a wide sense stationary random process representing a non-deterministic signal is

Question 4

Statement (I): Sinusoidal signals are used as basic function in electrical systems.
Statement (II): The response of a linear system to a sinusoidal input function remains sinusoidal.

Question 5

The governing differential equations connecting the output y(t) and the input x(t) of four continuous time systems are given in the List-I and List-II respectively. Match List-I (Equation) with List-II (System Category) and select the correct answer using the codes given below the lists:
List-I
A)

B)

C)

D)

List-II
1) Linear, time-invariant and dynamic
2) Non-linear, time-invariant and dynamic
3) Linear, time-variable and dynamic
4) Non-linear, time-variable and dynamic
5) Non-linear, time-invariant and non-dynamic

Question 6

is defined as

Determine the value of n for which

is guaranteed to be zero.

Question 7

Which one of the following systems described by the following input-output relations is non-linear?

Question 8

Which one of the following is correct? Energy of a power signal is

Question 9

A discrete-time system has input

and output

satisfying

The system is

Question 10

Consider an LTI system representing a passive electrical network. If the input is a sinusoidal signal, then the steady output of the network is

Question 11

The response of a system to a complex input

is specified as

The system

Question 12

In a discrete-time Low Pass Filter, the frequency response is

Question 13

The unit sample response of a discrete system is {1, 1/2, 1/4, 0, 0, 0,.....} For an input sequence {1, 0, 1, 0, 0, 0, ....} what is the output sequence?

Question 14

Consider the following statements about linear time invariant (LTI) continuous time systems:
1) The output signal in an LTI system with known input and known impulse response can always be determined.
2) A causal LTI system is always stable.
3) A stable LTI system has an impulse response, h(t) whichhas a finite value when integrated over whole of the time axis, i.e.

is finite.
Which of the statements given above are correct?

Question 15

Match List-I (CT Function) with List-II (CT Fourier Transform) and select the correct answer using the code given below the lists:
List-I
A)

B)

C)

D)

List-II
1)

2)

3)

4)

Question 16

If

is an even function, then what is its Fourier transform

?

Question 17

The relation between input

and output

of a continuous-time system is given by

What is the forced response of the system when

(a constant)?

Question 18

Match List-I (Time Function) with List-II (Fourier Spectrum/Fourier Transform) and select the correct answer using the codes given below the lists:
List-I
A) Periodic Function
B) Aperiodic Function
C) Unit Impulse

D) sin

List-II
1) Continuous spectrum at all frequencies
2)

3) Line discrete spectrum
4) 1

Question 19

A real signal

has Fourier transform

. Which one of the following is correct?

Question 20

Decimation is the process of

Question 21

Assertion (A): There are no convergence issues with the discrete-time Fourier series in general.
Reason (R): A discrete-time signal is always obtained by sampling a continuous-time signal.

Question 22

The discrete time Fourier transform (DTFT) of

is equal to

Question 23

For certain sequences which are neither absolutely summable nor square summalbe, it is possible to have a Fourier Transform (FT) representation if we

Question 24

Which one of the following is a Dirichlet condition?

Question 25

A unit impulse function

is defined by
1)

for all t except t = 0
2)

The Fourier transform

of

is

Question 26

A periodic function satisfies Dirichlet’s conditions. This implies that the function

Question 27

A waveform is given by

What will be the magnitude of the second harmonic in its Fourier series representation?

Question 28

For the discrete signal

the z-transform is

Question 29

The final value theorem is

Question 30

Match List-I (Discrete Time Signal) with List-II (Transform) and select the correct answer using the codes given below the lists:
List-I
A) Unit step function
B) Unit impulse function
C)

D)

List-II
1) 1
2)

3)

4)