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Determine the nature of the signal: x(t) = e^-0.2t [cosΩt + jsinΩt].

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in Signals and Systems by (1.2m points)
Determine the nature of the signal: x(t) = e^-0.2t [cosΩt + jsinΩt].

(a) Exponentially decaying sinusoidal signal

(b) Exponentially growing sinusoidal signal

(c) Sinusoidal signal

(d) Exponential signal

I had been asked this question in an international level competition.

Origin of the question is The Complex Exponential topic in section Signals and Systems Basics of Signals and Systems

1 Answer

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by (42.1k points)
Correct answer is (a) Exponentially decaying sinusoidal signal

Best explanation: Clearly the signal has negative exponential ⇒ Decaying exponential signal.

The signal also has sinusoidal component.

∴ The signal is exponentially decaying sinusoidal signal.

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