FSK

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[editar] FSK (Frequency Shift Keying)

Una señal FSK puede ser modelada como la suma de dos señales ASK, que son a su vez una codificacion unipolar NRZ modulada con un coseno.

FSKsignal.png


\begin{align} & s_{FSK}(t)=A_{c}\sum\limits_{k=-\infty }^{\infty }{p\left( t-kT_{s} \right)\cos \left( b_{k}\cdot \omega _{c}t \right)}=x_{ASK_{1}}(t)+x_{ASK_{2}}(t) \\ & s_{FSK}(t)=A_{c}\sum\limits_{k=-\infty }^{\infty }{a_{k1}p\left( t-kT_{s} \right)\cos \left( \omega _{c1}t \right)}+A_{c}\sum\limits_{k=-\infty }^{\infty }{a_{k2}p\left( t-kT_{s} \right)\cos \left( \omega _{c2}t \right)} \\ & b_{k}=\left\{ 1,2 \right\}\to \left\{ \begin{align} & 1\to a_{k1}=1;a_{k2}=0 \\ & 2\to a_{k1}=0;a_{k2}=1 \\ \end{align} \right. \\ & x_{I}(t)=\sum\limits_{k=-\infty }^{\infty }{a_{k}p\left( t-kT_{s} \right)},x_{Q}(t)=0 \\ & a_{'1'}=1,a_{'0'}=0 \\ & m_{a_{k}}=\frac{1}{2},P_{a_{k}}=\frac{1}{2},\sigma _{a_{k}}^{2}=\frac{1}{4} \\ & G_{I}(f)=\sigma _{a_{k}}^{2}\cdot R_{s}\left| P(f) \right|^{2}+m_{a_{k}}^{2}\cdot R_{s}^{2}\sum\limits_{k=-\infty }^{\infty }{\left| P(kR_{s}) \right|^{2}\delta \left( f-kR_{s} \right)} \\ & G_{I}(f)=G_{NRZ}(f)=\frac{A_{c}^{2}}{4}T_{s}\operatorname{sinc}^{2}\left( T_{s}f \right)+\frac{A_{c}^{2}}{4}\delta \left( f-R_{s} \right) \\ & G_{x}(f)=\frac{G_{I}(f-f_{c})+G_{I}(f+f_{c})}{4}+\frac{G_{Q}(f-f_{c})+G_{Q}(f+f_{c})}{4}\to \\ & G_{x}(f)=\frac{G_{I}(f-f_{c})+G_{I}(f+f_{c})}{4}=G_{x}(f)=\frac{G_{I}(f\pm f_{c})}{4} \\ & G_{x_{ASK1}}(f)=G_{x_{ASK2}}(f)=\frac{A_{c}^{2}}{4^{2}}T_{s}\operatorname{sinc}^{2}\left( T_{s}\left( f\pm f_{c} \right) \right)+\frac{A_{c}^{2}}{4^{2}}\delta \left( f\pm f_{c}-R_{s} \right)\to \\ & G_{FSK}(f)=\frac{A_{c}^{2}}{4^{2}}T_{s}\operatorname{sinc}^{2}\left( T_{s}\left( f\pm f_{c1} \right) \right)+\frac{A_{c}^{2}}{4^{2}}\delta \left( f\pm f_{c1}-R_{s} \right)+ \\ & \frac{A_{c}^{2}}{4^{2}}T_{s}\operatorname{sinc}^{2}\left( T_{s}\left( f\pm f_{c2} \right) \right)+\frac{A_{c}^{2}}{4^{2}}\delta \left( f\pm f_{c2}-R_{s} \right) \\ \end{align}


Para la probabilidad de error (BER):

BER de FSK


Proyecto: Departamento de Teoría de la Señal y Comunicaciones
Anterior: PSK — FSK — Siguiente: QAM


Obtenido de "http://es.wikiversity.org/wiki/FSK"
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