(FT) The Fourier transformation is a mathematical procedure to separate out the frequency components of a signal from its amplitudes as a function of time, or the inverse Fourier transformation (IFT) calculates the time domain from the frequency domain. The FT is used to generate the spectrum from the free induction decay or spin echo in the pulse MR technique and is essential to most MR imaging techniques. The Fourier transformation can be generalized to multiple dimensions, e.g. to relate an image to its corresponding k-space representation, or to include chemical shift information in some chemical shift imaging techniques. Fourier transformation analysis allows spatial information to be reconstructed from the raw data.

(FFT) A particularly fast and efficient computational method of performing a Fourier transformation, which is the mathematical process by which raw data is processed into a usable image.

MR imaging techniques in which at least one dimension is phase encoded by applying variable gradient pulses along that dimension before reading out the MR signal with a magnetic field gradient perpendicular to the variable gradient. The Fourier transformation is then used to reconstruct an image from the set of encoded MR signals. An imaging technique of this type is spin warp imaging.

See also Spin Warp Imaging.

Form of the Fourier transformation that reverses the process, e.g. if the Fourier transformation is used to analyze a function of time into its equivalent frequency components, the inverse Fourier transformation will synthesize that function of time from these frequency components.

(3D FT) A specialized 3D imaging technique that uses computer processing to combine individual slice acquisitions together to produce an image that represents length, width and height.