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. Author manuscript; available in PMC: 2011 Oct 1.
Published in final edited form as: J Magn Reson Imaging. 2010 Oct;32(4):943–952. doi: 10.1002/jmri.22308

Figure 8.

Figure 8

Multipoint decomposition is a transform from the temporal domain to the spectral domain, much like the Discrete Fourier Transform (DFT). For cases with equally spaced echoes and equally spaced chemical shifts, the decomposition is in fact a special case of the DFT. The frequency response of three-echo water/fat decomposition is shown here (solid lines) against the frequency response of a three-point DFT (dashed line). The first two terms of the DFT correspond exactly to the water (blue) and fat (orange) estimates, and the third term (green line) represents a modeled species with a chemical shift opposite that of fat.