FSK

FSK (Frequency Shift Keying)

Una señal FSK puede ser modelada como la suma de dos señales ASK, que son a su vez una codificación unipolar NRZ modulada con un coseno.

$\begin{matrix} s_{F S K} (t) = A_{c} \sum_{k = - \infty}^{\infty} p (t - k T_{s}) \cos (b_{k} \cdot ω_{c} t) = x_{A S K_{1}} (t) + x_{A S K_{2}} (t) \\ s_{F S K} (t) = A_{c} \sum_{k = - \infty}^{\infty} a_{k 1} p (t - k T_{s}) \cos (ω_{c 1} t) + A_{c} \sum_{k = - \infty}^{\infty} a_{k 2} p (t - k T_{s}) \cos (ω_{c 2} t) \\ b_{k} = {1, 2} \to {\begin{matrix} 1 \to a_{k 1} = 1; a_{k 2} = 0 \\ 2 \to a_{k 1} = 0; a_{k 2} = 1 \end{matrix} \\ x_{I} (t) = \sum_{k = - \infty}^{\infty} a_{k} p (t - k T_{s}), x_{Q} (t) = 0 \\ a_{' 1^{'}} = 1, a_{' 0^{'}} = 0 \\ m_{a_{k}} = \frac{1}{2}, P_{a_{k}} = \frac{1}{2}, σ_{a_{k}}^{2} = \frac{1}{4} \\ G_{I} (f) = σ_{a_{k}}^{2} \cdot R_{s} {| P (f) |}^{2} + m_{a_{k}}^{2} \cdot R_{s}^{2} \sum_{k = - \infty}^{\infty} {| P (k R_{s}) |}^{2} δ (f - k R_{s}) \\ G_{I} (f) = G_{N R Z} (f) = \frac{A_{c}^{2}}{4} T_{s} {sinc}^{2} (T_{s} f) + \frac{A_{c}^{2}}{4} δ (f - R_{s}) \\ G_{x} (f) = \frac{G_{I} (f - f_{c}) + G_{I} (f + f_{c})}{4} + \frac{G_{Q} (f - f_{c}) + G_{Q} (f + f_{c})}{4} \to \\ G_{x} (f) = \frac{G_{I} (f - f_{c}) + G_{I} (f + f_{c})}{4} = G_{x} (f) = \frac{G_{I} (f \pm f_{c})}{4} \\ G_{x_{A S K 1}} (f) = G_{x_{A S K 2}} (f) = \frac{A_{c}^{2}}{4^{2}} T_{s} {sinc}^{2} (T_{s} (f \pm f_{c})) + \frac{A_{c}^{2}}{4^{2}} δ (f \pm f_{c} - R_{s}) \to \\ G_{F S K} (f) = \frac{A_{c}^{2}}{4^{2}} T_{s} {sinc}^{2} (T_{s} (f \pm f_{c 1})) + \frac{A_{c}^{2}}{4^{2}} δ (f \pm f_{c 1} - R_{s}) + \\ \frac{A_{c}^{2}}{4^{2}} T_{s} {sinc}^{2} (T_{s} (f \pm f_{c 2})) + \frac{A_{c}^{2}}{4^{2}} δ (f \pm f_{c 2} - R_{s}) \end{matrix}$

Para la probabilidad de error (BER):

BER de FSK

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FSK

FSK (Frequency Shift Keying)

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