Signal And Systems Set 2

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| By Rejimano

Rejimano

Community Contributor

Quizzes Created: 2 | Total Attempts: 261

Questions: 10 | Attempts: 98 | Updated: Dec 26, 2023

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Signal and Systems Set 2
Contains 10 Questions

Questions and Answers

1.

What is the output y(n) when a signal x(n)=n*u(n)is passed through a accumulator system under the conditions that it is initially relaxed?
- A.
  
  (n2+n+1)/2
- B.
  
  (n(n+1))/2
- C.
  
  (n2+n+2)/2
- D.
  
  None of the mentioned
Correct Answer
B. (n(n+1))/2

Explanation
Given that the system is initially relaxed, that is y(-1)=0
According to the equation of the accumulator,

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2.

If the output of the system of the system at any ‘n’ depends only the present or the past values of the inputs then the system is said to be:
- A.
  
  Linear
- B.
  
  Non-Linear
- C.
  
  Causal
- D.
  
  Non-causal
Correct Answer
C. Causal

Explanation
A system is said to be causal if the output of the system is defined as the function shown below
y(n)=F[x(n),x(n-1),x(n-2),…] So, according to the conditions given in the question, the system is a causal system.

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3.

The discrete time function defined as u(n)=n for n≥0;=0 for n<0 is an:
- A.
  
  Unit sample signal
- B.
  
  Unit step signal
- C.
  
  Unit ramp signal
- D.
  
  None of the mentioned
Correct Answer
C. Unit ramp signal

Explanation
When we plot the graph for the given function, we get a straight line passing through origin with a unit positive slope. So, the function is called as unit ramp signal.

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4.

X(n)*δ(n-k)=?
- A.
  
  X(n)
- B.
  
  X(k)
- C.
  
  X(k)*δ(n-k)
- D.
  
  x(k)*δ(k)
Correct Answer
C. X(k)*δ(n-k)

Explanation
The given signal is defined only when n=k by the definition of delta function. So, x(n)*δ(n-k)= x(k)*δ(n-k).

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5.

Zero-input response is also known as Natural or Free response.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
For a zero-input response, the input is zero and the output of the system is independent of the input of the system. So, the response if such system is also known as Natural or Free response

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6.

The solution obtained by assuming the input x(n) of the system is zero is:
- A.
  
  General solution
- B.
  
  Particular solution
- C.
  
  Complete solution
- D.
  
  Homogenous solution
Correct Answer
D. Homogenous solution

Explanation
By making the input x(n)=0 we will get a homogenous difference equation and the solution of that difference equation is known as Homogenous or Complementary solution

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7.

What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0?
- A.
  
  (-1)n-1 + (4)n-2
- B.
  
  (-1)n+1 + (4)n+2
- C.
  
  (-1)n+1 + (4)n-2
- D.
  
  None of the mentioned
Correct Answer
B. (-1)n+1 + (4)n+2

Explanation
Explanation: Given difference equation is y(n)-3y(n-1)-4y(n-2)=0—-(1)
Let y(n)=λn
Substituting y(n) in the given equation
=>λn – 3λn-1 – 4λn-2 = 0
=> λn-2(λ2 – 3λ – 4) = 0
the roots of the above equation are λ=-1,4
Therefore, general form of the solution of the homogenous equation is

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8.

For a signal x(n) to exhibit even symmetry, it should satisfy the condition | X(-ω)|=| X(ω)|.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
We know that, if a signal x(n) is real, then
X*(ω)=X(-ω)

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9.

What is the energy density spectrum Sxx(ω) of the signal x(n)=anu(n), |a|<1?
- A.
  
  1/(1+2acosω+a2 )
- B.
  
  1/(1+2asinω+a2 )
- C.
  
  1/(1-2asinω+a2 )
- D.
  
  1/(1-2acosω+a2 )
Correct Answer
A. 1/(1+2acosω+a2 )

Explanation
Since |a|

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10.

If a power signal has its power density spectrum concentrated about zero frequency, the signal is known as:
- A.
  
  Low frequency signal
- B.
  
  Middle frequency signal
- C.
  
  High frequency signal
- D.
  
  None of the mentioned
Correct Answer
A. Low frequency signal

Explanation
We know that, for a low frequency signal, the power signal has its power density spectrum concentrated about zero frequency.

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Current Version
Dec 26, 2023

Quiz Edited by
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Mar 09, 2018

Quiz Created by
Rejimano

Signal And Systems Set 2

What is the output y(n) when a signal x(n)=n*u(n)is passed through a accumulator system under the conditions that it is initially relaxed?

If the output of the system of the system at any ‘n’ depends only the present or the past values of the inputs then the system is said to be:

The discrete time function defined as u(n)=n for n≥0;=0 for n<0 is an:

X(n)*δ(n-k)=?

Zero-input response is also known as Natural or Free response.

The solution obtained by assuming the input x(n) of the system is zero is:

What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0?

For a signal x(n) to exhibit even symmetry, it should satisfy the condition | X(-ω)|=| X(ω)|.

What is the energy density spectrum Sxx(ω) of the signal x(n)=anu(n), |a|<1?

If a power signal has its power density spectrum concentrated about zero frequency, the signal is known as: