Modulaciones digitales

$\begin{matrix} s_{A S K} (t) = A_{c} \sum_{k = - \infty}^{\infty} a_{k} p (t - k T_{s}) \cos (ω_{c} t) \\ s_{P S K} (t) = A_{c} \sum_{k = - \infty}^{\infty} p (t - k T_{s}) \cos (ω_{c} t + φ_{k}) = \\ A_{c} \sum_{k = - \infty}^{\infty} p (t - k T_{s}) \cos (ω_{c} t) \underset{I_{k}}{\underset{⏟}{\cos (φ_{k})}} - A_{c} \sum_{k = - \infty}^{\infty} p (t - k T_{s}) \sin (ω_{c} t) \underset{Q_{k}}{\underset{⏟}{\sin (φ_{k})}} \\ s_{Q A M} (t) = A_{c} \sum_{k = - \infty}^{\infty} a_{k} p (t - k T_{s}) \cos (ω_{c} t + φ_{k}) = \\ A_{c} \sum_{k = - \infty}^{\infty} a_{k} \underset{I_{k}}{\underset{⏟}{\cos (φ_{k})}} p (t - k T_{s}) \cos (ω_{c} t) - A_{c} \sum_{k = - \infty}^{\infty} a_{k} \underset{Q_{k}}{\underset{⏟}{\sin (φ_{k})}} p (t - k T_{s}) \sin (ω_{c} t) \\ s_{F S K} (t) = A_{c} \sum_{k = - \infty}^{\infty} p (t - k T_{s}) \cos (b_{k} \cdot ω_{c} t) = x_{A S K_{1}} (t) + x_{A S K_{2}} (t) \\ s_{M S K} (t) = A_{c} \sum_{k = - \infty}^{\infty} a_{I_{k}} \cos (\frac{π}{2 T_{b}} t) p (t - k T_{s}) \cos (ω_{c} t) - A_{c} \sum_{k = - \infty}^{\infty} a_{Q_{k}} \sin (\frac{π}{2 T_{b}} t) p (t - k T_{s}) \sin (ω_{c} t) \end{matrix}$

Sabiendo que:

$\begin{matrix} x_{m} (t) = x_{I} (t) \cos (ω_{c} t) - x_{Q} (t) \sin (ω_{c} t) \\ R_{x_{I} x_{Q}} (τ) = R_{x_{Q} x_{I}} (τ) \\ R_{x} (τ) = R_{I} (τ) \frac{\cos (ω_{c} τ)}{2} + R_{Q} (τ) \frac{\cos (ω_{c} τ)}{2} \to \\ G_{x} (f) = \frac{G_{I} (f - f_{c}) + G_{I} (f + f_{c})}{4} + \frac{G_{Q} (f - f_{c}) + G_{Q} (f + f_{c})}{4} \end{matrix}$

Constelación

Las señales digitales suelen visualizarse mediante su constelación:

$\begin{matrix} x_{m} (t) = x_{I} (t) \cos (ω_{c} t) - x_{Q} (t) \sin (ω_{c} t) \\ {\tilde{x}}_{m} (t) = x_{I} (t) + j \cdot x_{Q} (t) \end{matrix}$

Se representa en un plano:

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Modulaciones digitales

Constelación

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