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$\begin{align} & \hat{x}(t)=x(t)*h_{hilbert}(t)=\int_{-\infty }^{\infty }{\frac{x(\tau )}{\pi (t-\tau )}}\partial \tau \text{ }\to \text{ }\hat{X}(f)=X(f)\left( -j\operatorname{sign}(f) \right) \\ & R_{yx}(\tau )=R_{xy}^{*}(\tau )\text{ };\text{ }G_{{\hat{x}}}(f)=G_{x}(f)\text{ ; }R_{\hat{x}x}(\tau )=-R_{x\hat{x}}(\tau ) \\ & x_{+}(t)=x(t)+j\hat{x}(t) \\ & x_{-}(t)=x(t)-j\hat{x}(t) \\ & X_{+}(f)=\left\{ \begin{align} & 2X(f),f>0 \\ & 0,f<0 \\ \end{align} \right.=X(f)\left( 1+\operatorname{sign}(f) \right) \\ & X_{-}(f)=\left\{ \begin{align} & 0,f>0 \\ & 2X(f),f<0 \\ \end{align} \right.=X(f)\left( 1-\operatorname{sign}(f) \right) \\ & G_{x_{+}}(f)=\left\{ \begin{align} & 4G_{x}(f),f>0 \\ & 0,f<0 \\ \end{align} \right.=2G_{x}(f)\left( 1+\operatorname{sign}(f) \right) \\ & G_{x_{-}}(f)=\left\{ \begin{align} & 0,f>0 \\ & 4G_{x}(f),f<0 \\ \end{align} \right.=2G_{x}(f)\left( 1-\operatorname{sign}(f) \right) \\ & S_{x_{+}}=S_{x_{-}}=2S_{x} \\ & R_{x_{+}x_{-}}(\tau )=0 \\ & \tilde{x}(t)=x_{+}(t)e^{-j\omega _{c}t}\text{ ; }\tilde{X}(f)=X_{+}(f+f_{c}) \\ & \tilde{Y}\left( f \right)=\frac{\tilde{X}\left( f \right)\cdot \tilde{H}\left( f \right)}{2} \\ & \tilde{x}(t)=x_{I}(t)+jx_{Q}(t)=e(t)e^{j\varphi (t)} \\ & x(t):\text{ Se }\!\!\tilde{\mathrm{n}}\!\!\text{ al paso-banda} \\ & \tilde{x}(t),x_{I}(t),x_{Q}(t),e(t)\text{ : Se }\!\!\tilde{\mathrm{n}}\!\!\text{ ales paso-bajo} \\ & x_{I}(t)=\text{Componente en fase de }x(t)\text{ }(I:\text{ In phase)} \\ & x_{Q}(t)=\text{Componente en cuadratura de }x(t)\text{ }(Q:\text{ Quadrature)} \\ & e(t)=\text{ Envolvente (el modulo) de }x(t) \\ & \varphi (t)=\text{ Fase de }x(t)\text{ } \\ & x(t)=x_{I}(t)\cos (\omega _{c}t)-x_{Q}(t)\sin (\omega _{c}t)=e(t)\cos (\omega _{c}t+\varphi (t)) \\ & e(t)=\left| \tilde{x}(t) \right|=\sqrt{x_{I}^{2}(t)+x_{Q}^{2}(t)}=\sqrt{x^{2}(t)+\hat{x}^{2}(t)} \\ & \varphi (t)=\arctan \left( \frac{x_{Q}(t)}{x_{I}(t)} \right) \\ & x_{I}(t)=e(t)\cos \left( \varphi (t) \right)\text{ ; }x_{Q}(t)=e(t)\sin \left( \varphi (t) \right) \\ & G_{x_{I}}(f)={}^{1}\!\!\diagup\!\!{}_{4}\;\left( G_{x_{+}}(f+f_{c})+G_{x_{-}}(f-f_{c}) \right) \\ & S_{x}=S_{I}=S_{Q} \\ \end{align}$

	$s (t)$	$S (f)$
AM	$A_{c}\left( 1+mx(t) \right)\cos \left( \omega _{c}t \right)$	$\frac{A_{c}}{2}\left( \delta \left( f-f_{c} \right)+\delta (f+f_{c}) \right)+\frac{A_{c}}{2}m\left( X\left( f-f_{c} \right)+X(f+f_{c}) \right)$
DSB	$A c x (t)cos(ω c t)$	$\frac{A_{c}^{2}}{4}\left( G_{x}(f-f_{c})+G_{x}(f+f_{c}) \right)$
SSB	$\frac{A_{c}}{2}\left( x(t)\cos (\omega _{c}t)-\hat{x}(t)\sin (\omega _{c}t) \right)$	$\frac{A_{c}}{4}\left[ X(f-f_{c})\left( 1+\operatorname{sign}(f-f_{c}) \right) \right]+\left[ X(f+f_{c})\left( 1-\operatorname{sign}(f+f_{c}) \right) \right]$
PM	$\begin{align} & A_{c}\cos \left( \omega _{c}t+\varphi _{\Delta }x(t) \right) \\ & x_{\begin{smallmatrix} PM \\ FM \end{smallmatrix}}^{tone}(t)=s(t)=A_{c}\sum\limits_{k=-\infty }^{\infty }{J_{k}\left( \beta \right)\cos \left( \omega _{c}t+k\omega _{m}t \right)} \\ \end{align}$	$S^{tone}(f)=\frac{A_{c}}{2}\sum\limits_{k=-\infty }^{\infty }{J_{k}\left( \beta \right)\left[ \delta \left( f-\left( f_{c}+kf_{m} \right) \right)+\delta \left( f+\left( f_{c}+kf_{m} \right) \right) \right]}$
FM	$\begin{align} & A_{c}\cos \left( \omega _{c}t+2\pi f_{\Delta }\int_{-\infty }^{t}{x\left( \lambda \right)\partial \lambda } \right) \\ & x_{\begin{smallmatrix} PM \\ FM \end{smallmatrix}}^{tone}(t)=s(t)=A_{c}\sum\limits_{k=-\infty }^{\infty }{J_{k}\left( \beta \right)\cos \left( \omega _{c}t+k\omega _{m}t \right)} \\ \end{align}$	$S^{tone}(f)=\frac{A_{c}}{2}\sum\limits_{k=-\infty }^{\infty }{J_{k}\left( \beta \right)\left[ \delta \left( f-\left( f_{c}+kf_{m} \right) \right)+\delta \left( f+\left( f_{c}+kf_{m} \right) \right) \right]}$

	$G s (f)$	$P s$	$β T$	$\left( {}^{S}\!\!\diagup\!\!{}_{N}\; \right)_{D}$
AM	$\frac{A_{c}^{2}}{4}\left( \delta (f-f_{c})+\delta (f+f_{c}) \right)+\frac{A_{c}^{2}}{4}\cdot m^{2}\left( G_{x}(f-f_{c})+G_{x}(f+f_{c}) \right)$	$\frac{A_{c}^{2}}{2}\left( 1+m^{2}S_{x} \right)$	$2 W$	$\frac{m^{2}S_{x}}{1+m^{2}S_{x}}\gamma$
DSB	$\frac{A_{c}^{2}}{4}\left( G_{x}(f-f_{c})+G_{x}(f+f_{c}) \right)$	$\frac{A_{c}^{2}}{2}S_{x}$	$2 W$	$γ$
SSB	$\frac{A_{c}^{2}}{8}\left[ G_{x}(f-f_{c})\left( 1+\operatorname{sign}(f-f_{c}) \right) \right]+\left[ G_{x}(f+f_{c})\left( 1-\operatorname{sign}(f+f_{c}) \right) \right]$	$\frac{A_{c}^{2}}{4}S_{x}$	$W$	$γ$
PM	$\frac{A_{c}^{2}}{4}\sum\limits_{k=-\infty }^{\infty }{\left\| J_{k}\left( \beta \right) \right\|^{2}\left[ \delta \left( f-\left( f_{c}+kf_{m} \right) \right)+\delta \left( f+\left( f_{c}+kf_{m} \right) \right) \right]}$	$\frac{A_{c}^{2}}{2}$	$\begin{align} & 2\left( \beta _{\begin{smallmatrix} PM \\ FM \end{smallmatrix}}+1 \right)W= \\ & 2\left( \varphi _{\Delta }A_{m}+1 \right)W \\ \end{align}$	$\varphi _{\Delta }^{2}S_{x}\gamma$
FM	$\frac{A_{c}^{2}}{4}\sum\limits_{k=-\infty }^{\infty }{\left\| J_{k}\left( \beta \right) \right\|^{2}\left[ \delta \left( f-\left( f_{c}+kf_{m} \right) \right)+\delta \left( f+\left( f_{c}+kf_{m} \right) \right) \right]}$	$\frac{A_{c}^{2}}{2}$	$\begin{align} & 2\left( \beta _{\begin{smallmatrix} PM \\ FM \end{smallmatrix}}+1 \right)W= \\ & 2\left( \frac{A_{m}f_{\Delta }}{f_{m}}+1 \right)W \\ \end{align}$	$3\left( \frac{f_{\Delta }}{W} \right)^{2}S_{x}\gamma$

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