#### In-depth |

## Spectrum of CPFSK

The spectrum of the CPFSK signal also changes as a function of the frequency spacing between the two symbol states and how the phase trajectory is controlled when changing from one frequency to another. A detailed mathematical description (see in-depth) of the spectral response for CPFSK can be found in Proakis (1989), and we shall consider only two special cases known as Sunde's FSK and Minimum Shift Keying (MSK). Sunde's FSK arises when the spacing between the two symbol frequencies is made exactly equal to the symbol rate. For this case, the spectrum uniquely contains two discrete spectral lines at the two symbol frequencies, in addition to a broad spectral spread. These spectral lines can be used in a coherent FSK detector as the source of the carrier references, often extracted using a phase-locked loop. |

Minimum Shift Keying employs a symbol spacing equal to one half of the symbol rate and produces a smooth spectrum with narrow main lobe and rapidly reducing side-lobe energy. This narrow symbol spacing means that MSK can be more spectrally efficient than binary ASK and PSK, and in fact approaches the performance of quadrature phase shift keying (QPSK) systems. The price to be paid for this excellent performance is increased complexity in the generation and detection process compared with Sunde's FSK, for example.

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