Difference between revisions of "User:CSeguinot"

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And here's some following text to the formulas.
 
And here's some following text to the formulas.
  
The equivalent baseband representation help us for the simulation of bandpass signals. At this step we need some math. We will consider a carrier modulated in phase and/or amplitude (in the sake of simplicity, Frequency modulation is not considered but it can be related to phase modulation.). Such a modulated signal m(t) and it's complex representation is :
 
  
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Such a modulated signal ''m(t)'' and it's complex representation <math>\tilde{m}(t)</math> is :
  
The complex representation is obtained by replacing the cos function by an exponent function. The real signal correspond to the real part of the complex signal .
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:: <math>m(t)=a(t) \cos(2\pi F_0t + \phi(t))</math>
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:: <math>\tilde{m}(t)=a(t) e^{(j(2\pi F_0t + \phi(t)))} = a(t) e^{j \phi(t)} e^{j2\pi F_0t}</math>
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The complex representation is obtained by replacing the cos function by an exponent function. The real signal correspond to the real part of the complex signal <math>m(t)=\text{Re}(\tilde{m}(t))</math>.

Revision as of 20:55, 20 January 2021

This page is a temporary test

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And here's some following text to the formulas.


Such a modulated signal m(t) and it's complex representation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \tilde{m}(t)} is :

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle m(t)=a(t) \cos(2\pi F_0t + \phi(t))}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \tilde{m}(t)=a(t) e^{(j(2\pi F_0t + \phi(t)))} = a(t) e^{j \phi(t)} e^{j2\pi F_0t}}


The complex representation is obtained by replacing the cos function by an exponent function. The real signal correspond to the real part of the complex signal Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle m(t)=\text{Re}(\tilde{m}(t))} .