Test: Signal & Systems- 3

Question 1

The even part of the signal x(n) = u(n)

Accepted Answer

Answer

1

Answer

1/2

Answer

1 + &delta;(n)

Question 2

The value of discrete time signal at non-integer is :

Accepted Answer

Zero

Answer

Undefined

Answer

Same as the value of previous integer

Answer

1

Question 3

The ROC of the signal x(t) = 4

Accepted Answer

Does not exist

Answer

Re (s) > 0

Answer

Re (s) < 0

Answer

Whole s-plane

Question 4

The input and output relationship of a system is described as y(t) = ax + b, this system is linear

Accepted Answer

for any value of a and b = 0

Answer

for any value of a and b

Answer

for any value of a and b > 0

Answer

for any value of a and b < 0

Question 5

Which of the following signal is an example of an anti causal signal

Accepted Answer

e-at u(-t)

Answer

e-at u(t)

Answer

e^-at u(t-4)

Answer

e^-at u(t+4)

Question 6

The maximum phase-shift provided by the given system is

Accepted Answer

- 900

Answer

+ 900

Answer

+ 1800

Answer

- 1800

Question 7

Determine the fundamental period of x(n) =

Accepted Answer

12

Answer

6

Answer

24

Answer

4

Question 8

Consider a signal x(t) = 4 rect (t/6) and its Fourier - transform is x(ω). Determine the area under the curve in the ω-domain.

Accepted Answer

24

Answer

&infin;

Answer

8&pi;

Answer

4

Question 9

If the Fourier transform of x(t) is x(ω), then determine the Fourier transform of x(at-b)

Accepted Answer

Answer

Answer

Answer

Question 10

A pole zero pattern of a certain filter is shown in the figure. The filter must be

Accepted Answer

APF

Answer

LPF

Answer

BPF

Answer

HPF

Question 11

Determine the laplace-transform of signal x(t) shown in figure

Accepted Answer

Answer

Answer

Answer

Question 12

Determine the total energy of x(t) = 12 Sinc (6t)

Accepted Answer

24 units

Answer

&infin; units

Answer

0 unit

Answer

12.5 units

Question 13

Determine the bandwidth of the signal x(t) = e^-at u(t), so that it contains 90% of its total energy.

Accepted Answer

6.31a

Answer

8.13a

Answer

&infin;

Answer

11.24a

Question 14

Determine the output y(t) for an input x(t) = e^-2t u(t), if the step response of the system is t u(t).

Accepted Answer

(1/2){1 - e^-2t} u(t)

Answer

{1 - e^-2t} u(t)

Answer

2 {1 - e^-2t} u(t)

Answer

{e^-2t - 1} u(t)

Question 15

Simplify the following expression:
δ(-t) * u(t) * e^-t/2 u(t)

Accepted Answer

2 {1 - e^-t/2} u(t)

Answer

2 {1 - e^2t} u(t)

Answer

2 {1 - e^2t} u(-t)

Answer

2 {1 + e^2t} u(-t)

Question 16

Consider the analog signal x(t) = 3 Cos 100πt. This signal is sampled with a frequency of 75 samples per second and at the reconstruction side an ideal LPF having cut-off frequency is 30Hz is used. Determine the frequency component at the output of filter.

Accepted Answer

25 Hz

Answer

50 Hz

Answer

0 Hz

Answer

75 Hz

Question 17

The input and output relationship of a system is given as,

Accepted Answer

Causal, Linear and Unstable

Answer

Causal, Linear and Stable

Answer

Non Causal, Linear and Stable

Answer

Causal, Non-Linear and Unstable

Question 18

A signal x(t) = 2 (1 - Cos2πt) is sampled with a sampling frequency of 10 Hz. Determine the z-transform of sampled signal.

Accepted Answer

Answer

Answer

Answer

None of these

Question 19

Given,

Determine the ROC of its z-transform.

Accepted Answer

|Z| > 1/3

Answer

|Z| > 1

Answer

|Z| < 1

Answer

|Z| < 1/3

Question 20

If a signal f(t) has energy E, the energy of the signal f(2t) is equal to

Accepted Answer

E/2

Answer

E

Answer

2E

Answer

4E

Question 21

The correlation between two signals x₁(t) and x₂(t) is 6. If average power of x₁(t) is 10 and x₂(t) is 8.
Then determine the power of x₁(t) + x₂(t)

Accepted Answer

30

Answer

18

Answer

24

Answer

12

Question 22

, the co-efficient of term e-t in f(t) will be :

Accepted Answer

2/3

Answer

0

Answer

0.5

Answer

1

Question 23

S₁ : δ(n) is an energy signal having energy is 1.

S₂ : u(n) is a power signal having power is 1/2.

Which of the above is/are correct?

Accepted Answer

Both S₁ and S₂ are correct

Answer

S₁ is correct and S₂ is incorrect

Answer

S₁ is incorrect and S₂ is correct

Answer

Both S₁ and S₂ are incorrect

Question 24

The input and output relationship of a system is given as,

The system is :

Accepted Answer

Linear, Unstable, Non-Causal

Answer

Linear, Stable, Causal

Answer

Linear, Unstable, Causal

Answer

Non-Linear, Unstable, Non-Causal

Question 25

Determine the impulse response of the inverse system, if the impulse response of the system is u(n).

Accepted Answer

δ(n) - δ(n-1)

Answer

u(-n-1)

Answer

u(n) - u(n-1)

Answer

u(-n)

GATE Electrical Engineering (EE) Test: Signal & Systems- 3 Free Online

MCQ Practice Test & Solutions: Test: Signal & Systems- 3 (25 Questions)

The even part of the signal x(n) = u(n)

The value of discrete time signal at non-integer is :

The ROC of the signal x(t) = 4

The input and output relationship of a system is described as y(t) = ax + b, this system is linear

Which of the following signal is an example of an anti causal signal

The maximum phase-shift provided by the given system is

Determine the fundamental period of x(n) =

Consider a signal x(t) = 4 rect (t/6) and its Fourier - transform is x(ω). Determine the area under the curve in the ω-domain.

If the Fourier transform of x(t) is x(ω), then determine the Fourier transform of x(at-b)

A pole zero pattern of a certain filter is shown in the figure. The filter must be

Determine the laplace-transform of signal x(t) shown in figure

Determine the total energy of x(t) = 12 Sinc (6t)

Determine the bandwidth of the signal x(t) = e^-at u(t), so that it contains 90% of its total energy.

Determine the output y(t) for an input x(t) = e^-2t u(t), if the step response of the system is t u(t).

Simplify the following expression:
δ(-t) * u(t) * e^-t/2 u(t)

Consider the analog signal x(t) = 3 Cos 100πt. This signal is sampled with a frequency of 75 samples per second and at the reconstruction side an ideal LPF having cut-off frequency is 30Hz is used. Determine the frequency component at the output of filter.

The input and output relationship of a system is given as,

A signal x(t) = 2 (1 - Cos2πt) is sampled with a sampling frequency of 10 Hz. Determine the z-transform of sampled signal.

Given,

Determine the ROC of its z-transform.

If a signal f(t) has energy E, the energy of the signal f(2t) is equal to

The correlation between two signals x₁(t) and x₂(t) is 6. If average power of x₁(t) is 10 and x₂(t) is 8.
Then determine the power of x₁(t) + x₂(t)

, the co-efficient of term e-t in f(t) will be :

S₁ : δ(n) is an energy signal having energy is 1.
S₂ : u(n) is a power signal having power is 1/2.
Which of the above is/are correct?

The input and output relationship of a system is given as,
The system is :

Determine the impulse response of the inverse system, if the impulse response of the system is u(n).

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GATE Electrical Engineering (EE) Test: Signal & Systems- 3 Free Online

MCQ Practice Test & Solutions: Test: Signal & Systems- 3 (25 Questions)

The even part of the signal x(n) = u(n)

The value of discrete time signal at non-integer is :

The ROC of the signal x(t) = 4

The input and output relationship of a system is described as y(t) = ax + b, this system is linear

Which of the following signal is an example of an anti causal signal

The maximum phase-shift provided by the given system is

Determine the fundamental period of x(n) =

Consider a signal x(t) = 4 rect (t/6) and its Fourier - transform is x(ω). Determine the area under the curve in the ω-domain.

If the Fourier transform of x(t) is x(ω), then determine the Fourier transform of x(at-b)

A pole zero pattern of a certain filter is shown in the figure. The filter must be

Determine the laplace-transform of signal x(t) shown in figure

Determine the total energy of x(t) = 12 Sinc (6t)

Determine the bandwidth of the signal x(t) = e-at u(t), so that it contains 90% of its total energy.

Determine the output y(t) for an input x(t) = e-2t u(t), if the step response of the system is t u(t).

Simplify the following expression: δ(-t) * u(t) * e-t/2 u(t)

Consider the analog signal x(t) = 3 Cos 100πt. This signal is sampled with a frequency of 75 samples per second and at the reconstruction side an ideal LPF having cut-off frequency is 30Hz is used. Determine the frequency component at the output of filter.

The input and output relationship of a system is given as,

A signal x(t) = 2 (1 - Cos2πt) is sampled with a sampling frequency of 10 Hz. Determine the z-transform of sampled signal.

Given, Determine the ROC of its z-transform.

If a signal f(t) has energy E, the energy of the signal f(2t) is equal to

The correlation between two signals x1(t) and x2(t) is 6. If average power of x1(t) is 10 and x2(t) is 8. Then determine the power of x1(t) + x2(t)

, the co-efficient of term e-t in f(t) will be :

S1 : δ(n) is an energy signal having energy is 1.S2 : u(n) is a power signal having power is 1/2.Which of the above is/are correct?

The input and output relationship of a system is given as,The system is :

Determine the impulse response of the inverse system, if the impulse response of the system is u(n).

GATE Electrical Engineering (EE) Mock Test Series 2027

GATE Electrical Engineering (EE) Mock Test Series 2027

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About this Electrical Engineering (EE) Practice Test

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Determine the bandwidth of the signal x(t) = e^-at u(t), so that it contains 90% of its total energy.

Determine the output y(t) for an input x(t) = e^-2t u(t), if the step response of the system is t u(t).

Simplify the following expression:
δ(-t) * u(t) * e^-t/2 u(t)

Given,

Determine the ROC of its z-transform.

The correlation between two signals x₁(t) and x₂(t) is 6. If average power of x₁(t) is 10 and x₂(t) is 8.
Then determine the power of x₁(t) + x₂(t)

S₁ : δ(n) is an energy signal having energy is 1.
S₂ : u(n) is a power signal having power is 1/2.
Which of the above is/are correct?

The input and output relationship of a system is given as,
The system is :