Consider the system shown in the figure below. The transfer function $$\frac{{Y\left( z \right)}}{{X\left( z \right)}}$$ of the system is<br><img src="/images/question-image/electronics-and-communications-engineering/signal-processing/1681537187-consider-the-system-shown-in-the.jpg" title="Signal Processing mcq question image" alt="Signal Processing mcq question image">

Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ - \infty }^\infty {x\left( {t - \tau } \right)} h\left( {2\tau } \right)d\tau $$
Signal Processing mcq question image

Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.

A

Causal, LP

B

BIBO, LTI

C

BIBO, Causal, LTI

D

LP, LTI

For the discrete-time system shown in the figure, the poles of the system transfer function are located at
Signal Processing mcq question image

A

2, 3

B

$$\frac{1}{2},3$$

C

$$\frac{1}{2},\frac{1}{3}$$

D

$$2,\frac{1}{3}$$

The function x(t) is shown in the figure. Even and odd parts of a unit-step function u(t) are respectively,
Signal Processing mcq question image

A

$$\frac{1}{2},\frac{1}{2}x\left( t \right)$$

B

$$ - \frac{1}{2},\frac{1}{2}x\left( t \right)$$

C

$$\frac{1}{2}, - \frac{1}{2}x\left( t \right)$$

D

$$ - \frac{1}{2}, - \frac{1}{2}x\left( t \right)$$

The impulse response and the excitation function of a linear time invariant causal system are shown in figure (a) and (b) respectively. The output of the system at t = 2 sec is equal to
Signal Processing mcq question image

A

0

B

$$\frac{1}{2}$$

C

$$\frac{3}{2}$$

D

1

Laplace transform of the function f(t) is given by $${\text{F}}\left( {\text{s}} \right) = {\text{L}}\left\{ {{\text{f}}\left( {\text{t}} \right)} \right\} = \int_0^\infty {{\text{f}}\left( {\text{t}} \right){{\text{e}}^{ - {\text{st}}}}{\text{dt}}{\text{.}}} $$ Laplace transform of the function shown below is given by
Transform Theory mcq question image

A

$$\frac{{1 - {{\text{e}}^{ - 2{\text{s}}}}}}{{\text{s}}}$$

B

$$\frac{{1 - {{\text{e}}^{ - {\text{s}}}}}}{{2{\text{s}}}}$$

C

$$\frac{{2 - 2{{\text{e}}^{ - {\text{s}}}}}}{{\text{s}}}$$

D

$$\frac{{1 - 2{{\text{e}}^{ - {\text{s}}}}}}{{\text{s}}}$$

The Laplace transform of the causal periodic square wave of period T shown in the figure below is It
Signal Processing mcq question image

A

$$F\left( s \right) = \frac{1}{{1 + {e^{ - \frac{{sT}}{2}}}}}$$

B

$$F\left( s \right) = \frac{1}{{s\left( {1 + {e^{ - \frac{{sT}}{2}}}} \right)}}$$

C

$$F\left( s \right) = \frac{1}{{s\left( {1 - {e^{ - \frac{{sT}}{2}}}} \right)}}$$

D

$$F\left( s \right) = \frac{1}{{1 - {e^{ - sT}}}}$$

The graph of a function f(x) is shown in the figure.
Probability and Statistics mcq question image

For f(x) to be valid probability density function, the value of h is

A

$$\frac{1}{3}$$

B

$$\frac{2}{3}$$

C

1

D

3

The circuit shown in the figure below function as
Electronics mcq question image

A

an OR gate

B

an AND gate

C

a NOR gate

D

a NAND gate

A rectangular pulse train s(t) as shown in the figure is convolved with the signal cos²(4π × 10³t). The convolved signal will be a
Signal Processing mcq question image

A

DC

B

12 kHz sinusoid

C

8 kHz sinusoid

D

14 kHz sinusoid

The magnitude and phase of the complex Fourier series coefficient a_k of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex number, R is the set of purely real numbers, and P is the set of purely imaginary numbers.
Signal Processing mcq question image

A

$$x\left( t \right) \in R$$

B

$$x\left( t \right) \in P$$

C

$$x\left( t \right) \in \left( {C - R} \right)$$

D

The information given is not sufficient to draw any conclusion about x(t)

Consider the system shown in the figure below. The transfer function $$\frac{{Y\left( z \right)}}{{X\left( z \right)}}$$ of the system is

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