Signal And Systems Set 2

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Quizzes Created: 2 | Total Attempts: 249
Questions: 10 | Attempts: 94

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Signal And Systems Set 2 - Quiz


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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