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  • Question
  • Consider a stable and causal system with impulse response h(t) and system function H(S). Suppose H(S) is rational, contains a pole at S = - 2, and does not have a zero at the origin. The location of all other poles and zero is unknown for each of the following statements. Let us determine whether statement is true or false.

    1. f[h(t) e-3t] converges
    2. Consider a stable and causal system with impulse response h(t) and system function H(S). Suppose H(S
    3. h(t) has finite duration
    4. H(s) = H(- s)
    Choose correct option.


  • Options
  • A. 1 - True, 2 - False, 3 - True, 4 - False
  • B. 1 - False, 2 - False, 3 - False, 4 - True
  • C. 1 - False, 2 - False, 3 - False, 4 - False
  • D. 1 - True, 2 - can't say, 3 - True, 4 - can't say

  • Correct Answer
  • 1 - False, 2 - False, 3 - False, 4 - False 

    Explanation
    Statement 1 is false, since f{h(t)e3t} corresponds to the value of the Laplace transform of h(t) at s = 3.

    If this converges, it implies that s = - 3 is in the ROC.

    A casual and stable system must always have its ROC to the right of all its poles. However, s = - 3 is not to the right of the pole at s = - 2.

    Statement 2 is false, because it is equivalent to stating that H(0) = 0. This contradicts the fact that H(s) does not have a zero at the origin.

    Statement 3 is false. If h(t) is of finite duration, then if its Laplace transform has any points in its ROC, ROC must be the entire s-plane.

    However, this is not consistent with H(s) having a pole at s = - 2.

    Statement 4 is false. If it were true, then H(s) has a pole at s = - 2, it must also have a pole at s = 2.

    This is inconsistent with the fact that all the poles of a causal and stable system must be in the left half of the s-plane.


    More questions

    • 1. A radar has a maximum range of 120 km. The maximum allowable pulse repetition frequency for unambiguous reception is

    • Options
    • A. 1250
    • B. 330
    • C. 2500
    • D. 8330
    • Discuss
    • 2. An unmodulated voltage 10 V effective is applied to a dioxide detector in which load resistance is 4 x 10-5 ohms. A micrometer shows that the rectified DC current in this resistance is 30 A. The input resistance of the detector is

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    • A. 114 kW
    • B. 336 kW
    • C. 384 kW
    • D. 455 kW
    • Discuss
    • 3. For a BJT a = 0.98, then ? =

    • Options
    • A. 0.02
    • B. 0.5
    • C. 4.9
    • D. 48
    • Discuss
    • 4. If the temperature of an extrinsic semiconductor is increased so that the intrinsic carrier concentration is doubled, then

    • Options
    • A. the majority carrier density is doubled
    • B. the minority carrier density is doubled
    • C. the minority carrier density becomes 4 times the original value
    • D. both the majority and minority carrier densities double
    • Discuss
    • 5. A cycloconverter is

    • Options
    • A. ac-dc converter
    • B. dc-ac converter
    • C. dc-dc converter
    • D. ac-ac converter
    • Discuss
    • 6. Consider the following DO statement in Fortran 77

      DO 52 N = 1, 10, 3

      The number of DO loop executions in the above statement is

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    • 7. In a single phase semiconverter feeding a highly inductive load, the load current is

    • Options
    • A. sinusoidal
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    • C. absolutely constant
    • D. rectangular
    • Discuss
    • 8. If ton and toff are the turn on and turn off times of a thyristor, then

    • Options
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    • B. ton >> toff
    • C. toff >> ton
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    • Discuss
    • 9. Which inverter circuit uses coupled inductors?

    • Options
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    • C. Modified McMurray Bedford half bridge inverter
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    • 10. If there are no permanent dipoles in a dielectric material, the dielectric constant is independent of temperature.

    • Options
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