Gaussian frequency-shift keying

Gaussian Frequency-Shift Keying (GFSK) is a type of Frequency Shift Keying modulation that uses a Gaussian filter to smooth positive/negative frequency deviations, which represent a binary 1 or 0. It is used by DECT, Bluetooth, Cypress WirelessUSB, Nordic Semiconductor, Texas Instruments LPRF, z-wave and Wavenis devices. For basic data rate Bluetooth the minimum deviation is 115 kHz.

Generalization

In a GFSK modulator, everything is the same as an FSK modulator except that before the baseband pulses (−1, +1) go into the FSK modulator, it is passed through a gaussian filter to make the pulse smoother so to limit its spectral width. Gaussian filtering is one of the very standard ways for reducing the spectral width, it is called "pulse shaping".

If we use −1 for $f_c - f_d$ and +1 for $f_c + f_d$, once when we jump from −1 to +1 or +1 to −1, the modulated waveform changes rapidly, which introduces large out-of-band spectrum. If we change the pulse going from −1 to +1 as −1, −.98, −.93 ..... +.96, +.99, +1, and we use this smoother pulse to modulate the carrier, the out-of-band spectrum will be reduced.