2011
DOI: 10.1007/128_2011_186
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Generalized Fourier Transform for Non-Uniform Sampled Data

Abstract: Fourier transform can be effectively used for processing of sparsely sampled multidimensional data sets. It provides the possibility to acquire NMR spectra of ultra-high dimensionality and/or resolution which allow easy resonance assignment and precise determination of spectral parameters, e.g., coupling constants. In this chapter, the development and applications of non-uniform Fourier transform is presented.

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Cited by 31 publications
(28 citation statements)
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“…which reflects the limits of sampling [41]. For the simplicity of its FT, the step function is time-symmetric here, which does not however contradicts the causality of the signal.…”
Section: Resolution Enhancementmentioning
confidence: 95%
See 1 more Smart Citation
“…which reflects the limits of sampling [41]. For the simplicity of its FT, the step function is time-symmetric here, which does not however contradicts the causality of the signal.…”
Section: Resolution Enhancementmentioning
confidence: 95%
“…Radial sampling is utilized in projection spectroscopy, and requires the algebraic decoding of peak frequencies [29][30][31][32][33] or the reconstruction of the full multidimensional spectrum [34][35][36][37]. Sparse non-uniformly sampled data sets can be processed in some cases by zero-augmented discrete Fourier transformation (DFT) [38][39][40][41], compressed sensing (CS) [42,43], maximum entropy [44][45][46] or multidimensional decomposition [47][48][49] methods. Non-Fourier multidimensional NMR methods have been reviewed recently by Mobli and Hoch [50].…”
Section: Introductionmentioning
confidence: 99%
“…Spectra of both high dimensionality and high resolution reduce overlap and ensure good precision in the determination of peak positions, both of which are critical for resonance assignment procedures. Such spectra can be effectively acquired with the use of non-Cartesian sampling in evolution time space by dramatically reducing the number of acquired FIDs [recently reviewed in (Coggins et al 2010;Freeman and Kupče 2012;Hiller and Wider 2012;Hyberts et al 2012;Kazimierczuk et al 2010aKazimierczuk et al , 2012Maciejewski et al 2012;Orekhov and Jaravine 2011). One of the most general sampling schemes is random sampling, which allows for optimal resolution also in C4D experiments (Kazimierczuk et al 2009).…”
Section: Introductionmentioning
confidence: 99%
“…This method can be combined with TROSY approach (Salzmann et al, 1998(Salzmann et al, , 1999Yang & Kay, 1999) for application to large systems (> 30 kDa) to overcome the line-broadening problems. Adoption of methods like longitudinal relaxation optimized technique and non-uniform sampling for fast data collection Kazimierczuk et al, 2012) can easily be employed in the present case, which can further reduce the experimental time by an order of magnitude. Since the data is acquired in the form of a 2D spectrum, high spectral/digital resolution can still be achieved easily without spending much instrument time.…”
mentioning
confidence: 99%