The Complex Exponential MCQ

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• Determine the nature of the signal: x(t) = e-0.2t .
  ক

  . ] Exponentially decaying sinusoidal signal

  খ

  cosΩt + jsinΩt

  গ

  cosΩt + jsinΩt

  ঘ

  cosΩt + jsinΩt
• An exponentially growing sinusoidal signal is:
  ক

  σ = 0 and Ω = 0

  খ

  σ > 0 and Ω ≠ 0

  গ

  σ < 0 and Ω ≠ 0

  ঘ

  σ = 0 and Ω ≠ 0
• When is a complex exponential signal sinusoidal?
  ক

  σ =0 and Ω = 0

  খ

  σ < 0 and Ω = 0

  গ

  σ = 0 and Ω ≠ 0

  ঘ

  σ ≠ 0 and Ω ≠ 0
• A complex exponential signal is a decaying exponential signal when
  ক

  Ω = 0 and σ > 0

  খ

  Ω = 0 and σ = 0

  গ

  Ω ≠ 0 and σ < 0

  ঘ

  Ω = 0 and σ < 0
• The most general form of complex exponential function is:
  ক

  eσt

  খ

  eΩt

  গ

  est

  ঘ

  eat
• exp is periodic
  ক

  is periodic ] for any w

  খ

  jwn

  গ

  jwn

  ঘ

  jwn
• Define the fundamental period of the following signal x = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?
  ক

  = exp(2pi*j*n/3) + exp(3*pi*j*n/4)? ] 8

  খ

  n

  গ

  n

  ঘ

  n
• exp(jwt) is periodic
  ক

  for any w

  খ

  for any t

  গ

  for no w

  ঘ

  for no t
• What is the period of exp(2+pi*j/4)t?
  ক

  4

  খ

  8

  গ

  16

  ঘ

  20
• What is the power possessed by a signal exp(jwt)?
  ক

  1

  খ

  0.5

  গ

  1⁄w

  ঘ

  w
• Sinusoidal signals multiplied by decaying exponentials are referred to as
  ক

  Amplified sinusoids

  খ

  Neutralized sinusoids

  গ

  Buffered sinusoids

  ঘ

  Damped sinusoids
• Total energy possessed by a signal exp(jwt) is?
  ক

  2pi/w

  খ

  pi/w

  গ

  pi/2w

  ঘ

  2pi/3w
• What is the fundamental frequency of exp(2pi*w*j)?
  ক

  1pi*w

  খ

  2pi*w

  গ

  w

  ঘ

  2w
• What is the magnitude of exp(2+3j)?
  ক

  exp(2.3)

  খ

  exp(3)

  গ

  exp(2)

  ঘ

  exp(3/2)
• What is exp(j
  ক

  equal to, where j is the square root of unity? ] cos ja + jsin a

  খ

  sin a + jcos a

  গ

  cos j + a sin j

  ঘ

  cos a + jsin a