Resumen y tablas

$\begin{matrix} \hat{x} (t) = x (t) * h_{h i l b e r t} (t) = \int_{- \infty}^{\infty} \frac{x (τ)}{π (t - τ)} \partial τ \to \hat{X} (f) = X (f) (- j sign (f)) \\ R_{y x} (τ) = R_{x y}^{*} (τ); G_{\hat{x}} (f) = G_{x} (f); R_{\hat{x} x} (τ) = - R_{x \hat{x}} (τ) \\ x_{+} (t) = x (t) + j \hat{x} (t) \\ x_{-} (t) = x (t) - j \hat{x} (t) \\ X_{+} (f) = {\begin{matrix} 2 X (f), f > 0 \\ 0, f < 0 \end{matrix} = X (f) (1 + sign (f)) \\ X_{-} (f) = {\begin{matrix} 0, f > 0 \\ 2 X (f), f < 0 \end{matrix} = X (f) (1 - sign (f)) \\ G_{x_{+}} (f) = {\begin{matrix} 4 G_{x} (f), f > 0 \\ 0, f < 0 \end{matrix} = 2 G_{x} (f) (1 + sign (f)) \\ G_{x_{-}} (f) = {\begin{matrix} 0, f > 0 \\ 4 G_{x} (f), f < 0 \end{matrix} = 2 G_{x} (f) (1 - sign (f)) \\ S_{x_{+}} = S_{x_{-}} = 2 S_{x} \\ R_{x_{+} x_{-}} (τ) = 0 \\ \tilde{x} (t) = x_{+} (t) e^{- j ω_{c} t}; \tilde{X} (f) = X_{+} (f + f_{c}) \\ \tilde{Y} (f) = \frac{\tilde{X} (f) \cdot \tilde{H} (f)}{2} \\ \tilde{x} (t) = x_{I} (t) + j x_{Q} (t) = e (t) e^{j φ (t)} \\ x (t) : Se \tilde{n} al paso-banda \\ \tilde{x} (t), x_{I} (t), x_{Q} (t), e (t) : Se \tilde{n} ales paso-bajo \\ x_{I} (t) = Componente en fase de x (t) (I : In phase) \\ x_{Q} (t) = Componente en cuadratura de x (t) (Q : Quadrature) \\ e (t) = Envolvente (el modulo) de x (t) \\ φ (t) = Fase de x (t) \\ x (t) = x_{I} (t) \cos (ω_{c} t) - x_{Q} (t) \sin (ω_{c} t) = e (t) \cos (ω_{c} t + φ (t)) \\ e (t) = | \tilde{x} (t) | = \sqrt{x_{I}^{2} (t) + x_{Q}^{2} (t)} = \sqrt{x^{2} (t) + {\hat{x}}^{2} (t)} \\ φ (t) = \arctan (\frac{x_{Q} (t)}{x_{I} (t)}) \\ x_{I} (t) = e (t) \cos (φ (t)); x_{Q} (t) = e (t) \sin (φ (t)) \\ G_{x_{I}} (f) =^{1} ╱_{4} (G_{x_{+}} (f + f_{c}) + G_{x_{-}} (f - f_{c})) \\ S_{x} = S_{I} = S_{Q} \end{matrix}$

	$s (t)$	$S (f)$
AM	$A_{c} (1 + m x (t)) \cos (ω_{c} t)$	$\frac{A_{c}}{2} (δ (f - f_{c}) + δ (f + f_{c})) + \frac{A_{c}}{2} m (X (f - f_{c}) + X (f + f_{c}))$
DSB	$A_{c} x (t) \cos (ω_{c} t)$	$\frac{A_{c}^{2}}{4} (G_{x} (f - f_{c}) + G_{x} (f + f_{c}))$
SSB	$\frac{A_{c}}{2} (x (t) \cos (ω_{c} t) - \hat{x} (t) \sin (ω_{c} t))$	$\frac{A_{c}}{4} [X (f - f_{c}) (1 + sign (f - f_{c}))] + [X (f + f_{c}) (1 - sign (f + f_{c}))]$
PM	$\begin{matrix} A_{c} \cos (ω_{c} t + φ_{Δ} x (t)) \\ x_{\begin{matrix} P M \\ F M \end{matrix}}^{t o n e} (t) = s (t) = A_{c} \sum_{k = - \infty}^{\infty} J_{k} (β) \cos (ω_{c} t + k ω_{m} t) \end{matrix}$	$S^{t o n e} (f) = \frac{A_{c}}{2} \sum_{k = - \infty}^{\infty} J_{k} (β) [δ (f - (f_{c} + k f_{m})) + δ (f + (f_{c} + k f_{m}))]$
FM	$\begin{matrix} A_{c} \cos (ω_{c} t + 2 π f_{Δ} \int_{- \infty}^{t} x (λ) \partial λ) \\ x_{\begin{matrix} P M \\ F M \end{matrix}}^{t o n e} (t) = s (t) = A_{c} \sum_{k = - \infty}^{\infty} J_{k} (β) \cos (ω_{c} t + k ω_{m} t) \end{matrix}$	$S^{t o n e} (f) = \frac{A_{c}}{2} \sum_{k = - \infty}^{\infty} J_{k} (β) [δ (f - (f_{c} + k f_{m})) + δ (f + (f_{c} + k f_{m}))]$

	$G_{s} (f)$	$P_{s}$	$β_{T}$	${(^{S} ╱_{N})}_{D}$
AM	$\frac{A_{c}^{2}}{4} (δ (f - f_{c}) + δ (f + f_{c})) + \frac{A_{c}^{2}}{4} \cdot m^{2} (G_{x} (f - f_{c}) + G_{x} (f + f_{c}))$	$\frac{A_{c}^{2}}{2} (1 + m^{2} S_{x})$	$2 W$	$\frac{m^{2} S_{x}}{1 + m^{2} S_{x}} γ$
DSB	$\frac{A_{c}^{2}}{4} (G_{x} (f - f_{c}) + G_{x} (f + f_{c}))$	$\frac{A_{c}^{2}}{2} S_{x}$	$2 W$	$γ$
SSB	$\frac{A_{c}^{2}}{8} [G_{x} (f - f_{c}) (1 + sign (f - f_{c}))] + [G_{x} (f + f_{c}) (1 - sign (f + f_{c}))]$	$\frac{A_{c}^{2}}{4} S_{x}$	$W$	$γ$
PM	$\frac{A_{c}^{2}}{4} \sum_{k = - \infty}^{\infty} {\| J_{k} (β) \|}^{2} [δ (f - (f_{c} + k f_{m})) + δ (f + (f_{c} + k f_{m}))]$	$\frac{A_{c}^{2}}{2}$	$\begin{matrix} 2 (β_{\begin{matrix} P M \\ F M \end{matrix}} + 1) W = \\ 2 (φ_{Δ} A_{m} + 1) W \end{matrix}$	$φ_{Δ}^{2} S_{x} γ$
FM	$\frac{A_{c}^{2}}{4} \sum_{k = - \infty}^{\infty} {\| J_{k} (β) \|}^{2} [δ (f - (f_{c} + k f_{m})) + δ (f + (f_{c} + k f_{m}))]$	$\frac{A_{c}^{2}}{2}$	$\begin{matrix} 2 (β_{\begin{matrix} P M \\ F M \end{matrix}} + 1) W = \\ 2 (\frac{A_{m} f_{Δ}}{f_{m}} + 1) W \end{matrix}$	$3 {(\frac{f_{Δ}}{W})}^{2} S_{x} γ$

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