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Complex Exponential Signals
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Background
Sum of Sinusoids using Complex Exponential Signals
The Inverse Euler Formulas express the
and
functions in terms of complex exponentials:
A signal formed from the summation of sinusoids is given by:
where
and
.
Then by the inverse Euler relationships:
where
is the complex-conjugate of
.
Each sinusoid is represented by two rotating phasors, one with a positive frequency
and the other with
.
The two-sided spectrum of a signal composed of sinusoids is then given by:
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