Consider the one-sided exponential function fi(t) = Ae-atu(t), where u(t) is the unit step function, a>0, and A > 0. (0) (ii) (1) (iv) Sketch the waveform of the signal, fi(t), marking the axis carefully. Calculate the Fourier transform of fi(t). Calculate the energy, E₁, in the signal fi(t). Determine the frequency wm such that the energy contributed by the spectral components of all the frequencies w such that w ≤ wm is 95% of the total signal energy E₁. You may assume the relationship: d dx tan a (²-) = Q² + 7²

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Consider the one-sided exponential function fi(t)
u(t) is the unit step function, a > 0, and A > 0.
(1)
(ii)
(iv)
You may assume the relationship:
d
dr
Sketch the waveform of the signal, fi(t), marking the axis carefully.
Calculate the Fourier transform of fi(t).
Calculate the energy, E₁, in the signal fi(t).
Determine the frequency wm such that the energy contributed by the
spectral components of all the frequencies w such that w|≤ wm is
95% of the total signal energy E₁.
tan
-1
(²) =
=
=
=
Ae-at u(t), where
a
a² + x²
Transcribed Image Text:Consider the one-sided exponential function fi(t) u(t) is the unit step function, a > 0, and A > 0. (1) (ii) (iv) You may assume the relationship: d dr Sketch the waveform of the signal, fi(t), marking the axis carefully. Calculate the Fourier transform of fi(t). Calculate the energy, E₁, in the signal fi(t). Determine the frequency wm such that the energy contributed by the spectral components of all the frequencies w such that w|≤ wm is 95% of the total signal energy E₁. tan -1 (²) = = = = Ae-at u(t), where a a² + x²
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