Pre Assessment Test - Basics Of Signals And Systems

By DEVIE P

DEVIE P, Assistant Professor

Devie, a seasoned finance professional specializing in fintech and innovation. Known for driving strategic financial initiatives and fostering industry collaboration.

Quizzes Created: 1 | Total Attempts: 155

, Assistant Professor

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Questions: 11 | Attempts: 155 | Updated: Mar 20, 2023

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Questions and Answers

1.

All the real time natural signals are of which type?
- A.
  
  Discrete
- B.
  
  Continous
- C.
  
  Digital
Correct Answer
B. Continous

Explanation
Real time natural signals are analog which are always continous

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2.

Is analog signals are more flexible for easy transmission?
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
Digital signals are more flexible to transmit than analog signals

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3.

Select the conditions for the existence of Initial value theorem.
- A.
  
  If time t approaches to infinity then the function f(t) should exists.
- B.
  
  If time t approaches to zero then the function f(t) should vanish.
- C.
  
  If time t approaches to zero then the function f(t) should exists.
- D.
  
  If time t approaches to infinity then the function f(t) should vanish.
Correct Answer
C. If time t approaches to zero then the function f(t) should exists.

Explanation
The initial value theorem states that if a function f(t) is Laplace transformable and has a finite Laplace transform F(s), then the limit of f(t) as t approaches zero exists and is equal to the initial value of F(s) at s=0. Therefore, the condition for the existence of the initial value theorem is that if time t approaches zero, then the function f(t) should exist.

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4.

In the following conditions, for which Final value doesn’t exist.
- A.
  
  If the function sF(s)has the infinite pole
- B.
  
  If the function sF(s)has pole on origin
- C.
  
  If the function sF(s)has no zeros
- D.
  
  If the function sF(s)has pole at unity
Correct Answer
B. If the function sF(s)has pole on origin

Explanation
If the function sF(s) has a pole on the origin, it means that the denominator of the function has a factor of (s-0), which simplifies to just s. This indicates that the function has a singularity at s=0, causing it to blow up to infinity at that point. As a result, the final value of the function does not exist.

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5.

Expand the series ->(1 + x)^−1
- A.
  
  1 + x + x^2 + x^3 + x^4 + . . .
- B.
  
  1 − x + 2x^2 − 3x^3 + 4x^4 − . . .
- C.
  
  1 − x + x^2 − x^3 + x^4 − . . .
Correct Answer
C. 1 − x + x^2 − x^3 + x^4 − . . .

Explanation
The given series is an expansion of the expression (1 + x)^-1. This can be derived using the formula for the sum of an infinite geometric series, which is a/(1 - r), where a is the first term and r is the common ratio. In this case, the first term is 1 and the common ratio is -x. Thus, the series can be written as 1 + x + x^2 + x^3 + x^4 + ... which simplifies to 1 − x + x^2 − x^3 + x^4 − ...

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6.

Expand the below binomial series->(1 + x)^n
- A.
  
  1 + nx +[n(n − 1)/2!] x^2 +[n(n − 1)(n − 2)/3!] x^3 + . . .
- B.
  
  1 + nx +2[n(n − 1)/2!] x^2 +3[n(n − 1)(n − 2)/3!] x^3 + . . .
- C.
  
  1 - nx +[n(n − 1)/2!] x^2 +[n(n − 1)(n − 2)/3!] x^3 + . . .
- D.
  
  1 - nx +[n(n − 1)/2!] x^2 -[n(n − 1)(n − 2)/3!] x^3 - . . .
Correct Answer
A. 1 + nx +[n(n − 1)/2!] x^2 +[n(n − 1)(n − 2)/3!] x^3 + . . .

Explanation
The given answer is the correct expansion of the binomial series (1 + x)^n. It represents the terms of the series where each term is obtained by raising x to a power and multiplying it by the corresponding coefficient. The coefficients are derived from the binomial coefficient formula, which involves the values of n and the power of x in each term. The given answer correctly follows the pattern of increasing powers of x and the corresponding coefficients based on the binomial coefficient formula.

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7.

High Pass Filter allows the
- A.
  
  Frequency lesser than infinity
- B.
  
  Frequency less than cut-off frequency
- C.
  
  Frequency higher than infinity
- D.
  
  Frequency higher than cut-off frequency
Correct Answer
D. Frequency higher than cut-off frequency

Explanation
A high pass filter allows frequencies that are higher than the cut-off frequency to pass through while attenuating or blocking frequencies that are lower than the cut-off frequency. This means that any signal with a frequency higher than the cut-off frequency will be allowed to pass through the filter with minimal loss or distortion.

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8.

Transfer function of the system is defined as the
- A.
  
  Ratio of laplace transform of input to output response
- B.
  
  Ratio of laplace transform of input to output response with zero initial condition
- C.
  
  Ratio of laplace transform of output to input response with zero initial condition
- D.
  
  Ratio of laplace transform of output to input response
Correct Answer
C. Ratio of laplace transform of output to input response with zero initial condition

Explanation
The transfer function of a system is defined as the ratio of the Laplace transform of the output response to the Laplace transform of the input. The inclusion of "with zero initial condition" means that the system is assumed to start from a state where there is no initial energy or activity. This assumption allows for a more accurate representation of the system's behavior in response to the input. Therefore, the correct answer is the ratio of the Laplace transform of the output to the input response with zero initial condition.

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9.

Low pass filter eliminates frequencies ______________ than the cut-off frequency
- A.
  
  Higher
- B.
  
  Lower
Correct Answer
A. Higher

Explanation
A low pass filter eliminates frequencies that are higher than the cut-off frequency. This means that any frequencies above the cut-off frequency are attenuated or reduced in amplitude, while frequencies below the cut-off frequency are allowed to pass through with minimal attenuation. Therefore, the correct answer is "higher."

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DEVIE P |Assistant Professor |

Devie, a seasoned finance professional specializing in fintech and innovation. Known for driving strategic financial initiatives and fostering industry collaboration.

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Current Version
Mar 20, 2023

Quiz Edited by
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Dec 18, 2016

Quiz Created by
DEVIE P

Pre Assessment Test - Basics Of Signals And Systems

All the real time natural signals are of which type?

Is analog signals are more flexible for easy transmission?

Select the conditions for the existence of Initial value theorem.

In the following conditions, for which Final value doesn’t exist.

Expand the series ->(1 + x)^−1

Expand the below binomial series->(1 + x)^n

High Pass Filter allows the

Transfer function of the system is defined as the

Low pass filter eliminates frequencies ______________ than the cut-off frequency