# Sinusoidal Signals

Consider a continous-time signal

*x*(*t*) = cos(*ω*_{0}*
t*)

for some real constant * ω *_{0}.
Use Eulers relation to write this as a sum of two complex exponentials, and
then use linearity of the CTFT to find

*X*(*ω*) = *π*
* δ *(*ω* - *ω *_{0}
) + *π* * δ
*(*ω *+
*ω *_{0}
)

where *δ * is the Dirac delta function.
What this says is that a cosine in the time domain is concentrated at two frequencies
in the frequency domain, one the negative of the other (which should not be
surprising).