Increasing the dimensionality of NMR experiments strongly enhances the spectral resolution and provides invaluable direct information about atomic interactions. However, the price tag is high: long measurement times and heavy requirements on the computation power and data storage. We introduce sparse fast Fourier transform as a new method of NMR signal collection and processing, which is capable of reconstructing high quality spectra of large size and dimensionality with short measurement times, faster computations than the fast Fourier transform, and minimal storage for processing and handling of sparse spectra. The new algorithm is described and demonstrated for a 4D BEST-HNCOCA spectrum.
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