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<center><math>c(t) = e^{j(\omega_c t + \theta_c)}\!</math></center> | <center><math>c(t) = e^{j(\omega_c t + \theta_c)}\!</math></center> | ||
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| + | <math>\omega_c\!</math> is called the carrier frequency, and <math>\theta_c\!</math> is called the phase of the carrier. | ||
| + | |||
| + | Graphically, this equation looks as follows, | ||
| + | |||
| + | <math>x(t)\!</math> ----------> x --------> <math>x_p(t)\!</math> | ||
| + | ^ | ||
| + | | | ||
| + | | | ||
| + | <math>c(t) = e^{j(\omega_c t + \theta_c)}\!</math> | ||
Revision as of 16:17, 16 November 2008
Complex Exponential Modulation
Many communication systems rely on the concept of sinusoidal amplitude modulation, in which a complex exponential or a sinusoidal signal, $ c(t)\! $, has its amplitude modulated by the information-bearing signal, $ x(t)\! $. $ x(t)\! $ is the modulating signal, and $ c(t)\! $ is the carrier signal. The modulated signal, $ y(t)\! $, is the product of these two signals:
An important objective of amplitude modulation is to produce a signal whose frequency range is suitable for transmission over the communication channel that is to be used.
One important for of modulation is when a complex exponential is used as the carrier.
$ \omega_c\! $ is called the carrier frequency, and $ \theta_c\! $ is called the phase of the carrier.
Graphically, this equation looks as follows,
$ x(t)\! $ ----------> x --------> $ x_p(t)\! $ ^ | | $ c(t) = e^{j(\omega_c t + \theta_c)}\! $
