Resumen y tablas para modulaciones digitales

$\begin{matrix} {\bar{G}}_{x} (f) = σ_{x}^{2} \cdot R_{s} {| P (f) |}^{2} + m_{x}^{2} \cdot R_{s}^{2} \sum_{k = - \infty}^{\infty} {| P (k R_{s}) |}^{2} δ (f - k R_{s}) \end{matrix}$

$\begin{matrix} H (f) = H_{β} (f) * \frac{1}{R} \prod (\frac{f}{R}) = \frac{π}{4 β} \cos (\frac{π}{2 β} f) \prod (\frac{f}{2 β}) * \frac{1}{R} \prod (\frac{f}{R}) \\ h (t) = h_{β} (t) \cdot sinc (R t) = \frac{\cos (2 β π t)}{1 - {(4 β t)}^{2}} \cdot sinc (R t) \end{matrix}$

Con filtro optimo: $h_{R} (t) = p^{*} (T_{s} - t)$

$\begin{matrix} \int_{V_{T}}^{\infty} \frac{1}{\sqrt{2 π σ^{2}}} \cdot e^{\frac{- {(t - m)}^{2}}{2 σ^{2}}} \partial t = Q (\frac{| V_{T} - m |}{\sqrt{σ^{2}}}) \\ P_{e} = p r (' 0^{'} s e n t) \cdot p (^{e r r o r} ╱_{' 0^{'} s e n t}) + p r (' 1^{'} s e n t) \cdot p (^{e r r o r} ╱_{' 1^{'} s e n t}) = \\ p r (' 0^{'} s e n t) \cdot Q (\frac{| V_{T} - m_{' 0^{'}} |}{\sqrt{σ^{2}}}) + p r (' 1^{'} s e n t) \cdot Q (\frac{| V_{T} - m_{' 1^{'}} |}{\sqrt{σ^{2}}}) \\ s_{T} (t) = \sum_{k = 0}^{\infty} a_{k} p (t - k T_{s}) \\ m_{y_{P R} (t)} = \int_{0}^{T_{s}} s_{T} (t) k p^{*} (t) \partial t \\ σ_{y_{P R} (t)}^{2} = \frac{η}{2} \cdot E_{p (t)} = \frac{η}{2} \int_{0}^{T_{s}} p^{2} (t) \partial t \end{matrix}$

	$s (t)$	$a_{k}$	${\bar{G}}_{s} (f)$	$Q (x)$
Unipolar NRZ	$\sum_{k = 0}^{\infty} a_{k} p (t - k T_{s})$	$a_{k} = {0, + A}$	$\frac{A^{2}}{4} T_{s} {sinc}^{2} (T_{s} f) + \frac{A^{2}}{4} δ (f - R_{s})$	$Q (\sqrt{\frac{E_{b}}{η}})$
Unipolar RZ	$\sum_{k = 0}^{\infty} a_{k} p (t - k T_{s})$	$a_{k} = {0, + A}$	$\frac{A^{2}}{16} T_{s} {sinc}^{2} (\frac{T_{s}}{2} f) + \frac{A^{2}}{16} \sum_{k = - \infty}^{\infty} {sinc}^{2} (\frac{k}{2}) δ (f - k R_{s})$	$Q (\sqrt{\frac{E_{b}}{η}})$
Polar	$\sum_{k = 0}^{\infty} a_{k} p (t - k T_{s})$	$a_{k} = {- A, + A}$	$A^{2} T_{s} {sinc}^{2} (T_{s} f)$	$Q (\sqrt{\frac{2 E_{b}}{η}})$
Bipolar	$\sum_{k = 0}^{\infty} a_{k} p (t - k T_{s})$	$a_{k} = {0, \pm A}$	$\frac{A^{2}}{2} T_{s} {sinc}^{2} (T_{s} f)$	$≃ \frac{3}{2} Q (\sqrt{\frac{E_{b}}{η}})$
Manchester	$\sum_{k = 0}^{\infty} a_{k} p (t - k T_{s})$	$a_{k} = {- A, + A}$	$A^{2} T_{s} {sinc}^{2} (\frac{T_{s} f}{2}) \sin^{2} (π f \frac{T_{s}}{2})$	$Q (\sqrt{\frac{2 E_{b}}{η}})$
ASK(OOK)	$A_{c} \sum_{k = 0}^{\infty} a_{k} p (t - k T_{s}) \cos (ω_{c} t)$	$a_{k} = {0, + A}$	$\frac{A^{2}}{4^{2}} T_{s} {sinc}^{2} (T_{s} (f \pm f_{c})) + \frac{A^{2}}{4^{2}} δ (f \pm f_{c} - R_{s})$	$Q (\sqrt{\frac{E_{b}}{η}})$
BPSK(PRK)	$A_{c} \sum_{k = 0}^{\infty} a_{k} p (t - k T_{s}) \cos (ω_{c} t)$	$a_{k} = {- 1, + 1}$	$\frac{A^{2} T_{s} {sinc}^{2} (T_{s} (f \pm f_{c}))}{4}$	$Q (\sqrt{\frac{2 E_{b}}{η}})$
QPSK	$\begin{matrix} A_{c} \sum_{k = - \infty}^{\infty} a_{I_{k}} p (t - k T_{s}) \cos (ω_{c} t) \\ - A_{c} \sum_{k = - \infty}^{\infty} a_{Q_{k}} p (t - k T_{s}) \sin (ω_{c} t) \end{matrix}$	$\begin{matrix} a_{I_{k}} = {- \frac{1}{\sqrt{2}}, + \frac{1}{\sqrt{2}}} \\ a_{Q_{k}} = {- \frac{1}{\sqrt{2}}, + \frac{1}{\sqrt{2}}} \end{matrix}$	$\frac{A_{c}^{2}}{4} T_{s} {sinc}^{2} (T_{s} (f \pm f_{c}))$	$Q (\sqrt{\frac{2 E_{b}}{η}})$
MSK	$\begin{matrix} A_{c} \sum_{k = - \infty}^{\infty} a_{I_{k}} \cos (\frac{π}{2 T_{b}} t) p (t - k T_{s}) \cos (ω_{c} t) \\ - A_{c} \sum_{k = - \infty}^{\infty} a_{Q_{k}} \sin (\frac{π}{2 T_{b}} t) p (t - k T_{s}) \sin (ω_{c} t) \end{matrix}$	$\begin{matrix} a_{I_{k}} = {- A, + A} \\ a_{Q_{k}} = {- A, + A} \end{matrix}$	$A_{c}^{2} \frac{σ_{a_{k}}^{2}}{2} \cdot T_{b} {(\frac{4}{π})}^{2} {[\frac{\cos (2 T_{b} π (f \pm f_{c}))}{1 - {(4 T_{b} (f \pm f_{c}))}^{2}}]}^{2}$	$Q (\sqrt{\frac{2 E_{b}}{η}})$
M-PSK	$A_{c} \sum_{k = - \infty}^{\infty} p (t - k T_{s}) \cos (ω_{c} t + φ_{k})$	$\begin{matrix} a_{I_{k}} = \cos (\frac{π}{M} i); i = 1, 2, 3 . . . \\ a_{Q_{k}} = \sin (\frac{π}{M} i); i = 1, 2, 3 . . . \end{matrix}$	$\frac{A_{c}^{2}}{4} T_{s} {sinc}^{2} (T_{s} (f \pm f_{c}))$	$≃ Q (\sqrt{\frac{2 E_{s}}{η}} \sin (\frac{π}{M}))$
QAM	$\begin{matrix} A_{c} \sum_{k = - \infty}^{\infty} a_{I_{k}} p (t - k T_{s}) \cos (ω_{c} t) \\ - A_{c} \sum_{k = - \infty}^{\infty} a_{Q_{k}} p (t - k T_{s}) \sin (ω_{c} t) \end{matrix}$	$\begin{matrix} a_{I_{k}} = {\pm \frac{1}{\sqrt{2}}, \pm \frac{3}{\sqrt{2}}, . . .} \\ a_{Q_{k}} = {\pm \frac{1}{\sqrt{2}}, \pm \frac{3}{\sqrt{2}}, . . .} \end{matrix}$	$\frac{A_{c}^{2}}{2} σ_{a_{k}}^{2} \cdot T_{s} {sinc}^{2} (T_{s} f)$	$2 (1 - \frac{1}{\sqrt{M}}) \cdot Q (\sqrt{\frac{3}{M - 1} \frac{E_{s}}{η}})$
FSK	$\begin{matrix} A_{c} \sum_{k = - \infty}^{\infty} p (t - k T_{s}) \cos (b_{k} \cdot ω_{c} t) = \\ x_{A S K_{1}} (t) + x_{A S K_{2}} (t) \end{matrix}$	$a_{k} = {0, + A}$	$\begin{matrix} \frac{A_{c}^{2}}{4^{2}} T_{s} {sinc}^{2} (T_{s} (f \pm f_{c 1})) + \frac{A_{c}^{2}}{4^{2}} δ (f \pm f_{c 1} - R_{s}) + \\ \frac{A_{c}^{2}}{4^{2}} T_{s} {sinc}^{2} (T_{s} (f \pm f_{c 2})) + \frac{A_{c}^{2}}{4^{2}} δ (f \pm f_{c 2} - R_{s}) \end{matrix}$	$Q (\sqrt{\frac{E_{b}}{η}})$

Resumen y tablas para modulaciones digitales

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