6.2 Carrier frequency modulation

Frequency shift keying (fsk)

The data is impressed upon the carrier frequency. Therefore, the $M$ different signals are

The $M$ different signals have $M$ different carrier frequencies with possibly different phase angles since the generators ofthese carrier signals may be different. The carriers are

In case $\forall m, {}_m=0$

Therefore, the frequency spacing could be as small as $(f)=\frac{1}{2T}$ since $\mathrm{sinc}(x)=0$ if $x=(1)$ or $(2)$ .

If the signals are designed to be orthogonal then the average probability of error for binary FSK with optimum receiver is

Note that $\mathrm{sinc}(x)$ takes its minimum value not at $x=(1)$ but at $(1.4)$ and the minimum value is $-0.216$ . Therefore if $(f)=\frac{0.7}{T}$ then