Signal and systems miscellaneous

Signal and systems miscellaneous

Easy Questions
Moderate Questions
Difficult Questions

Signals and Systems

Signal and systems miscellaneous
  1. The unit sample response of a discrete system is 1 1/2 1/4 0 0 0 … For an input sequence 1 0 10 0 0 … what is the output sequence?








  1. View Hint View Answer Discuss in Forum

    Given that,

    h[n] = 1
    1
    1
    		 0 0 0 ............
    24

    x[n] = 1 0 1 0 0 0 ……
    y(n) can be calculated by using method given below:

    y[n] = 1
    1
    		 1 +
    1
    1
    1
    		 0 0 ............
    2424

    or
    y[n] = 1
    1
    5
    1
    1
    		 0 0 ............
    2424

    Hence, alternative (D) is the correct choice.

    Correct Option: D

    Given that,

    h[n] = 1
    1
    1
    		 0 0 0 ............
    24

    x[n] = 1 0 1 0 0 0 ……
    y(n) can be calculated by using method given below:

    y[n] = 1
    1
    		 1 +
    1
    1
    1
    		 0 0 ............
    2424

    or
    y[n] = 1
    1
    5
    1
    1
    		 0 0 ............
    2424

    Hence, alternative (D) is the correct choice.

  1. Consider the following statements about linear time invariant (LTI) continuous time systems:
    1. The output signal in an LTI system with known input and known impulse response can always be determined.
    2. A causal LTI system is always stable.
    3. A causal LTI system has an impulse response. h(t) which has a finite value when integrated h(t) over
    whole of the time axis, i.e., + ∞is finite.
    – ∞

    Which of the statements given above are correct?








  1. View Hint View Answer Discuss in Forum

    Since, it is not necessary true that causal system is always stable.
    Hence, alternative (D) is the correct choice.

    Correct Option: D

    Since, it is not necessary true that causal system is always stable.
    Hence, alternative (D) is the correct choice.

  1. In the graph shown below, which one of the following expresses v(t)?










  1. View Hint View Answer Discuss in Forum

    Slope of the given wave = 2/1
    Equation of triangular wave which cuts at point-6 on the y axis is r(t) = (2t – 6) u(t)

    Therefore, the expression of v(t) can be expressed as
    v(t) = (2t – 6) u(t – 3) – (2t – 6) u(t – 4)
    or
    v(t) = (2t – 6) [u(t – 3) – u(t – 4)]

    Correct Option: D

    Slope of the given wave = 2/1
    Equation of triangular wave which cuts at point-6 on the y axis is r(t) = (2t – 6) u(t)

    Therefore, the expression of v(t) can be expressed as
    v(t) = (2t – 6) u(t – 3) – (2t – 6) u(t – 4)
    or
    v(t) = (2t – 6) [u(t – 3) – u(t – 4)]

  1. The governing differential equations connecting the output y(t) and the input x (t) of four continuous time systems are given in the List-I and List-II respectively. Match List-I (Equation) with List-II (System Category) and select the correct answer using the code given below the Lists—








  1. View Hint View Answer Discuss in Forum

    (A) 2t
    dy
    		 + 4y = 2tx
    dt

    ● Since, there is no constant hence linear.
    ● t factor means time-variant.
    ● dy/dt term means dynamic which gives A → 3

    (B) y
    dy
    		 + 4y = 2x
    dt

    ● Since, there is no constant term mean linear
    ● No time varying term means time-invariant.
    ● dy/dt term means dynamic which gives B → 1
    Since, these options given only in code (C). So, no need to solve further.
    Hence, alternative (C) is the correct choice.

    Correct Option: C

    (A) 2t
    dy
    		 + 4y = 2tx
    dt

    ● Since, there is no constant hence linear.
    ● t factor means time-variant.
    ● dy/dt term means dynamic which gives A → 3

    (B) y
    dy
    		 + 4y = 2x
    dt

    ● Since, there is no constant term mean linear
    ● No time varying term means time-invariant.
    ● dy/dt term means dynamic which gives B → 1
    Since, these options given only in code (C). So, no need to solve further.
    Hence, alternative (C) is the correct choice.

  1. The lengths of two discrete time sequences x1(n) and x2(n) are 5 and 7, respectively. What is the maximum length of a sequence x1(n) x2(n)?








  1. View Hint View Answer Discuss in Forum

    Given length of sequence
    x1(n)= N1 = 5 and
    given length of sequence
    x2(n)= N2 = 7
    Maximum length of sequence
    x1(n) x2(n)= N1 + N2 – 1
    = 5 + 7 – 1
    = 11

    Correct Option: D

    Given length of sequence
    x1(n)= N1 = 5 and
    given length of sequence
    x2(n)= N2 = 7
    Maximum length of sequence
    x1(n) x2(n)= N1 + N2 – 1
    = 5 + 7 – 1
    = 11