Fast Fourier Transform Telescope is Tegmark and Zaldarriaga's name for a design for an all-digital synthetic-aperture telescope. It is a type of interferometer designed to be cheaper than standard telescope interferometers currently in use.
In 1868, Hippolyte Fizeau realized that the lenses and mirrors in a telescope perform a physical approximation of a Fourier transform. He noted that by using an array of small instruments it would be possible to measure the diameter of a star with the same precision as a single telescope which was as large as the whole array — a technique which later became known as astronomical interferometry. See History of astronomical interferometry.
In a 2008 paper, Tegmark and Zaldarriaga proposed a telescope design that dispenses altogether with the lenses and mirrors, relying instead on computers fast enough to perform all the necessary transforms. The concept is an all-digital telescope with an antenna consisting of a rectangular grid. Building radio telescopes this way should become feasible within a few years if Moore's law continues to hold. Eventually optical telescopes could also be built this way. This technique is already being used in radar applications.
This paper refers to an earlier telescope design from 1993 which took direct images of the Crab nebula at radio wavelengths using an eight-by-eight-pixel two-dimensional spatial FFT processor.