GFSK

GFSK is an acronym for Gaussian frequency-shift keying.  It's a type of frequency shift keying (FSK) modulation that uses a Gaussian filter to smooth positive/negative frequency deviations. Gaussian filtering is a common way to reduce spectral width. It's also used in GMSK. I got into some of this in my posts on Digital modes here.

Gaussian filtering, like Gaussian elimination and Gaussian functions come from linear algebra. In 1810,  Johann Carl Friedrich Gauss invented a lot of what we now call linear algebra. I won't get into this in too much detail.  The Gausian filters in GFSK have more to do with Gaussian functions, it's more related to geometry than algebra. A function reveals the probability that any real measurement will fall between any two real limits (a low and high value) and the probability curve approaches zero on either side of those limits. a comparison of probability density functions allows us to assign values within that rage with confidence. Here it's used outbound to shape the pulses to reduce spectral width.

In the case of GFSK the Gaussian filter is used to smooth positive and negative frequency deviations, which represent a binary 1 or 0. remember the amplitude is not varying (much), the frequency is shifting, just over a relatively narrow frequency band, the minimum deviation is only 115 kHz. In a technology like Bluetooth, where the frequency hops 1600 times a second, the pulses might be a bit messy. So GFSK has the advantage of reducing out-of-band spectrum.