(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(\omega_{C}t+\theta)= \frac{1}{2}\exp^{j\theta}</math>
+
<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>
 
<math>      = \frac{1}{2\pi}2\pi\delta(w-w_{c}) * X(w) = X(w-w_{c})</math> , where * is convolution
 
<math>      = \frac{1}{2\pi}2\pi\delta(w-w_{c}) * X(w) = X(w-w_{c})</math> , where * is convolution

Revision as of 19:55, 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)

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Amplitude Modulatioin of a Complex Exponential Carrier

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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} $ $ = \frac{1}{2\pi}2\pi\delta(w-w_{c}) * X(w) = X(w-w_{c}) $ , where * is convolution

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood