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1. Find the Magnitude and Phase values of [tex]f(t) = 5 e^t u(t)[/tex] for [tex]w = -4, -2, 0, 2, 4[/tex].

a) Magnitude = \{2.24, 1.21, 5, 1.21, 2.24\}
Phase = \{75.97, 63.4, 0, -63.4, -75.97\}

b) Magnitude = \{1.21, 2.24, 5, 2.24, 1.21\}
Phase = \{75.97, 63.4, 0, -63.4, -75.97\}

c) Magnitude = \{2.24, 1.21, 5, 1.21, 2.24\}
Phase = \{75.97, 63.4, 0, 63.4, 75.97\}

d) Magnitude = \{1.21, 2.24, 5, 2.24, 1.21\}
Phase = \{-75.97, -63.4, 0, -63.4, -75.97\}

e) Magnitude = \{2.24, 1.21, 5, 1.21, 2.24\}
Phase = \{-75.97, -63.4, 0, 63.4, 75.97\}

f) Magnitude = \{1.21, 2.24, 5, 2.24, 1.21\}
Phase = \{-75.97, -63.4, 0, 63.4, 75.97\}

Answer :

Final answer:

The Magnitude and Phase values of the given function f(t) = 5 etu(t) for w = -4,-2,0, 2, 4 are as follows:

  • Magnitude = {2.24, 1.21, 5, 1.21, 2.24}
  • Phase = {75.97, 63.4, 0, -63.4, -75.97}

Explanation:

To find the Magnitude and Phase values of the given function f(t) = 5 etu(t) for w = -4,-2,0, 2, 4, we can use the Fourier Transform. The Fourier Transform of an exponential function multiplied by the unit step function is given by F(w) = 1 / (jw + 1), where j is the imaginary unit.

Substituting the values of w into the Fourier Transform equation, we can calculate the Magnitude and Phase values:

  1. For w = -4: Magnitude = |F(-4)| = |1 / (-4j + 1)| = 2.24, Phase = arg(F(-4)) = arg(1 / (-4j + 1)) = 75.97 degrees
  2. For w = -2: Magnitude = |F(-2)| = |1 / (-2j + 1)| = 1.21, Phase = arg(F(-2)) = arg(1 / (-2j + 1)) = 63.4 degrees
  3. For w = 0: Magnitude = |F(0)| = |1 / (0j + 1)| = 5, Phase = arg(F(0)) = arg(1 / (0j + 1)) = 0 degrees
  4. For w = 2: Magnitude = |F(2)| = |1 / (2j + 1)| = 1.21, Phase = arg(F(2)) = arg(1 / (2j + 1)) = -63.4 degrees
  5. For w = 4: Magnitude = |F(4)| = |1 / (4j + 1)| = 2.24, Phase = arg(F(4)) = arg(1 / (4j + 1)) = -75.97 degrees

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