We review the development of our digital wide-band Fast Fourier
Transform Spectrometers (FFTS). In just a few years, FFTS back-ends
have become a new standard for heterodyne receivers, particularly in
the mm and sub-mm wavelength range. They offer high instantaneous
bandwidths with many thousands spectral channels on a small electronic
board. Our FFT spectrometers make use of the latest versions of GHz
analog-to-digital converters and the most complex field programmable
gate array (FPGA) chips commercially available today. The XFFTS is our
latest development step: The new spectrometer board is able to analyze
2.5 GHz of instantaneous bandwidth with up to 65536 (64k) spectral
channels. An early version of the XFFTS with 32k channels is already
in successful operation at APEX and SOFIA.