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# One Shot Marathon Series Test - Signals and Systems

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Question 1

The system described by following differential equation is

Question 2

Two signals x(t) and h(t) are defined as follows

x(t) = 0 |t| > T1

h(t) = 0 |t| > T2

x(t)*h(t) =0 |t| > T3

T3 will be

Question 3

What is the convolution of x1(t) = sin 3t u(t), x2(t) = cos2t u(t)

Question 4

Find the time signal corresponding to  .

Question 5

If xe(t) represents even part of signal x(t) and xo(t) represents odd part of signal x(t) then choose the correct expression for x(t).

Question 6

An input signal x(t) = 4 + cos (4πt) – sin(8πt) is is applied to an LTI system with impulse response Then the response is _______.

Question 7

Consider the interconnection of three LTI systems as shown in below figure.

Assume, h1[n] = u[n + 2], h2[n] = δ[n – 2]

h3[n] = u[n] – u[n – 2]

Then the impulse response of overall system at n = 2 is_______.

Question 8

A periodic signal f(t) is shown in the figure below.

The frequency of the 3rd harmonic of its spectrum is ________kHz.

Question 9

Consider two signals

and

If then is

Question 10Multiple Correct Options

Which of the following operations are true with respect to signals?

Here E = Even signal

O = odd signal

× = Multiplication of signals
[Multi Select Question]

Question 11

The relationship between the input x(t) and output y(t) of a system is described by the differential equation

The impulse response of the system is

Question 12

X(f) is signal that has a rational Laplace transform with exactly two poles located at s = — 1 and s = — 3. If g(t) = e2t x(t) and Fourier transform of g(t) i.e. G(jω) converges, then x(t) is

Question 13

The frequency response of a system for impulse sequence response

Question 14

Find inverse L.T. of

Question 15

The value of integral

Question 16

If δ[n] is a discrete time unit impulse function, then find the value of summation.

Question 17

Consider a discrete time signal x[n] as

the energy of conjugate symmetric part of signal x[n] is_____J.

Question 18

Consider a discrete time signal shown in figure below.

If y[n] = n x[n] then

will be_____

Question 19

Let x[n] be the periodic extension of the sequence δ[n] – δ[n – 2] with period 4. The DTFS coefficients of x[n] is such that A is

Question 20

Let, .

The LT of x(t) is X(s). Then value of x(1) is____?

Question 21

If and y[n] is defined as

What is value of y[2]

Question 22

The DTFT of is where the constant is

Question 23Multiple Correct Options

Consider the following system

The system is ____

Question 24Multiple Correct Options

Which of the following is/are correct.

Question 25

Given the z-transform X(Z)

=, the value of x [] is _________.

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