Widely used higher-dimensional Fourier transform (FT) NMR spectroscopy suffers from two major drawbacks: (i) The minimal measurement time of an N-dimensional FT NMR experiment, which is constrained by the need to sample N - 1 indirect dimensions, may exceed by far the measurement time required to achieve sufficient signal-to-noise ratios. (ii) The low resolution in the indirect dimensions severely limits the precision of the indirect chemical shift measurements. To relax on constraints arising from these drawbacks, we present here an acquisition scheme which is based on the phase-sensitive joint sampling of the indirect dimensions spanning a subspace of a conventional NMR experiment. This allows one to very rapidly obtain high-dimensional NMR spectral information. Because the phase-sensitive joint sampling yields subspectra containing "chemical shift multiplets", alternative data processing is required for editing the components of the multiplets. The subspectra are linearly combined using a so-called "G-matrix" and subsequently Fourier-transformed. The chemical shifts are multiply encoded in the resonance lines constituting the shift multiplets. This corresponds to performing statistically independent multiple measurements, and the chemical shifts can thus be obtained with high precision. To indicate that a combined G-matrix and FT is employed, we named the new approach "GFT NMR spectroscopy". GFT NMR opens new avenues to establish high-throughput protein structure determination, to investigate systems with a higher degree of chemical shift degeneracy, and to study dynamic phenomena such as slow folding of biological macromolecules in greater detail.