ISI (Inter Symbol Interference)

De Wikiversidad

\begin{align} & s(t)=\sum\limits_{k=-\infty }^{\infty }{a_{k}p\left( t-kT_{s} \right)} \\ & h_{e}(t)=p(t)*h_{c}(t)*h_{R}(t) \\ & s(t)=\sum\limits_{k=-\infty }^{\infty }{a_{k}h_{e}\left( t-kT_{s} \right)=a_{0}h_{e}(t)}+a_{1}h_{e}\left( t-T_{s} \right)+a_{2}h_{e}\left( t-2T_{s} \right)+... \\ & h_{e}(t=0)=h_{e\max }=1,\left. s(t) \right|_{t=nT_{s}}\to \\ & \left. s\left( t \right) \right|_{t=0}=s\left( 0 \right)=\sum\limits_{k=-\infty }^{\infty }{a_{k}h_{e}\left( -kT_{s} \right)}=a_{0}\underbrace{h_{e}(0)}_{=1}+a_{1}\underbrace{h_{e}\left( -T_{s} \right)}_{=0}+a_{2}=\underbrace{h_{e}\left( -2T_{s} \right)}_{=0}+... \\ & h_{e}\left( mT_{s} \right)=0,m\ne 0 \\ & h_{e}(t)\cdot \sum\limits_{k=-\infty }^{\infty }{\delta \left( t-kT_{s} \right)=}h_{e}(0)\delta \left( t \right)\Rightarrow \sum\limits_{k=-\infty }^{\infty }{\delta \left( t-kT_{s} \right)=}\sum\limits_{k=-\infty }^{\infty }{\frac{1}{T_{s}}e^{j2\pi f_{s}t}} \\ & H_{e}(f)*\frac{1}{T_{s}}\sum\limits_{k=-\infty }^{\infty }{\delta \left( f-kf_{s} \right)=}h_{e}(0) \\ & \frac{1}{T_{s}}\sum\limits_{k=-\infty }^{\infty }{H_{e}\left( f-kf_{s} \right)=}h_{e}(0)\to \sum\limits_{k=-\infty }^{\infty }{H_{e}\left( f-kf_{s} \right)=}h_{e}(0)T_{s}=cte. \\ \end{align}

\begin{align} & Ej. \\ & H_{e}(f)=\prod{\left( \frac{f}{2B} \right)}\to h_{e}(t)=2B\operatorname{sinc}\left( 2Bt \right),f_{s}=R_{s} \\ & h_{e}(t)\cdot \sum\limits_{k=-\infty }^{\infty }{\delta \left( t-kT_{s} \right)=}h_{e}(0)\delta \left( t \right)\Rightarrow \sum\limits_{k=-\infty }^{\infty }{H_{e}\left( f-kf_{s} \right)=}h_{e}(0)T_{s}=cte. \\ & T_{s}=\frac{1}{2B},\frac{2}{2B},\frac{3}{2B},...\to R_{s}=\frac{2B}{n}\left( {}^{simbolos}\!\!\diagup\!\!{}_{s}\; \right) \\ \end{align}


Proyecto: Departamento de Teoría de la Señal y Comunicaciones
Anterior: Pulso coseno alzado — ISI (Inter Symbol Interference) — Siguiente: Codificaciones digitales


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