Similarly, the Fourier transform of exponentially damped sine wave can be obtained as
(14.8-12)
In both cases we have dropped the impulse components in the spectrum since those
impulses can not come into action for any legitimate value of
ω
. We notice that damped
sinusoids are aperiodic waveforms with finite energy, whereas, undamped sinusoids are
aperiodic waveforms with infinite energy.
14.9 ZERO-STATE RESPONSE BY FREQUENCY-DOMAIN ANALYSIS
We have seen that all practical waveforms, periodic or aperiodic, possess frequency-domain
descriptions in the form of Fourier transforms. All waveforms can be synthesised from
sinusoids of different frequencies ...
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