Frequency shift keying#
Frequency shift keying (FSK) is a digital modulation scheme that uses two different frequencies to encode the \(0\)s and \(1\)s:
\[\begin{split}
\begin{align}
s_0(t) &= \cos(\omega_0 t) \\
s_1(t) &= \cos(\omega_1 t)
\end{align}
\end{split}\]
where \(\omega_0 \not= \omega_1\).
Minimum shift keying#
Demodulation#
The application note [Incorporated, 1998] assumes that
\[\begin{split}
\begin{align}
\omega_0 = \omega_c - \Delta\omega \\
\omega_1 = \omega_c + \Delta\omega
\end{align}
\end{split}\]
so that demodulation can happen by simply multiplying the received signal, \(r(t)\), by a delayed version of itself
\[
r(t)r(t-T) = \cos((\omega_c \pm \Delta\omega) t) \cos((\omega_c \pm \Delta\omega) (t- T) )
\]
where \(T \omega_c = \frac{\pi}{2}\) or \(T = \frac{\pi}{2\omega_c}\). That means
\[\begin{split}
\begin{align}
r(t)r(t-T) &= \cos((\omega_c \pm \Delta\omega) t + (\omega_c \pm \Delta\omega) (t- T) ) \cos((\omega_c \pm \Delta\omega) t - (\omega_c \pm \Delta\omega) (t- T) )\\
&= \cos(2\omega_c t \pm 2\Delta\omega t - (\omega_c \pm \Delta\omega)T) \cos( - (\omega_c \pm \Delta\omega)T )
\end{align}
\end{split}\]