(Synchronous Demodulation (with phase error) in the Frequency DomainAgain)
(Synchronous Demodulation (with phase error) in the Frequency DomainAgain)
 
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== Synchronous Demodulation (with phase error) in the Frequency DomainAgain ==
 
== Synchronous Demodulation (with phase error) in the Frequency DomainAgain ==
 
Demodulating signal has phase difference θw.r.t.the modulating signal
 
Demodulating signal has phase difference θw.r.t.the modulating signal
<math>COS(W_{C}t+\delta)</math>
+
 
<math>      = \frac{1}{2\pi}2\pi\delta(w-w_{c}) * X(w) = X(w-w_{c})</math> , where * is convolution
+
<math>cos(\omega_{C}t+\theta)= \frac{1}{2}e^{j\theta}e^{j\omega_{c}t}+\frac{1}{2}e^{-j\theta}e^{-j\omega_{c}t}</math>
 +
 
 +
fourier ====>
 +
 
 +
[[Image:aaaa_ECE301Fall2008mboutin.jpg]]
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[[Image:aaaaa_ECE301Fall2008mboutin.jpg]]

Latest revision as of 20:00, 17 November 2008

the concept of modulation

A ECE301Fall2008mboutin.jpg Why?

•More efficient to transmit E&M signals at higher frequencies

•Transmitting multiple signals through the same medium using different carriers

•Transmitting through “channels” with limited passbands

•Others...

How?

•Manymethods

•Focus here for the most part on Amplitude Modulation (AM)

B ECE301Fall2008mboutin.jpg

Amplitude Modulatioin of a Complex Exponential Carrier

C ECE301Fall2008mboutin.jpg

Demodulation of Complex Exponential AM

De ECE301Fall2008mboutin.jpg

Sinusoidal AM

G ECE301Fall2008mboutin.jpg F ECE301Fall2008mboutin.jpg Ab ECE301Fall2008mboutin.jpg Aaa ECE301Fall2008mboutin.jpg Asd ECE301Fall2008mboutin.jpg

Synchronous Demodulation (with phase error) in the Frequency DomainAgain

Demodulating signal has phase difference θw.r.t.the modulating signal

$ cos(\omega_{C}t+\theta)= \frac{1}{2}e^{j\theta}e^{j\omega_{c}t}+\frac{1}{2}e^{-j\theta}e^{-j\omega_{c}t} $

fourier ====>

Aaaa ECE301Fall2008mboutin.jpg Aaaaa ECE301Fall2008mboutin.jpg

Alumni Liaison

Recent Math PhD now doing a post-doctorate at UC Riverside.

Kuei-Nuan Lin