(Synchronous Demodulation (with phase error) in the Frequency DomainAgain)
(Synchronous Demodulation (with phase error) in the Frequency DomainAgain)
 
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<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>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 ====> <math>\pie^{j/theta}/delta(/omega-/omega_{c})+/pie^{-j/theta}/delta(/omerga-/omerga_{c})</math>
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fourier ====>  
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Latest revision as of 19:00, 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)

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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} $

fourier ====>

Aaaa ECE301Fall2008mboutin.jpg Aaaaa ECE301Fall2008mboutin.jpg

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva