Difference between revisions of "Sangwan Han ECE301Fall2008mboutin" - Rhea

Latest revision as of 06:37, 17 November 2008

Amplitude Modulation

Def:Amplitude modulation (AM) is a method of data onto an carrier waveform.The highest frequency of the modulating data is normally less than 10 percent of the carrier frequency.

$ x(t) \longrightarrow\otimes\longrightarrow y(t)=x(t)c(t) $

       $ \uparrow  $

     c(t)

x(t) : "information bearing signal"

c(t) : "carrier"

There are two important types of carriers which are "complex exponential" and "sinusoidal"

Complex expenetial

$ c(t) = e ^{j(\omega_c t + \theta_c)} $

$ \omega_c = $ Frequency of carrier

$ \theta_c = $ Phase of carrier

complex exponential modulation

$ y(t) = e^{j\omega_c t}x(t) $

$ y(\omega) = F(e^{j\omega_c t}x(t)) $

$ =\frac{1}{2 \pi}F(e^{j\omega_c t})X(\omega) $

$ =\frac{1}{2\pi} 2\pi \delta (\omega - \omega_c) * X(\omega) $

$ =X(\omega - \omega_c)\! $

Demodulate the complex exponential

$ y(t) \longrightarrow\otimes\longrightarrow x(t) $

       $ \uparrow  $

     $ e^{-j\omega_ct} $

$ y(t) = e^{j\omega_c t}x(t) $

$ e^{-j\omega_c t}y(t) = e^{-j\omega_c t}e^{j\omega_c t}x(t) $

$ =x(t)\! $

Source

http://searchcio-midmarket.techtarget.com