Wiktor Koźmiński

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Application of Fourier Transform for processing 3D NMR spectra with random sampling of evolution time space is presented. The 2D FT is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Signal to noise ratios and linewidths for different random distributions were investigated by simulations and experiments.(More)
The detailed description of rules for generation of different random sampling schemes is shown and discussed with regard to Multidimensional Fourier Transform (MFT). The influence of different constrained random sampling schedules on FT of constant signal, i.e., Point Spread Function (PSF), is analyzed considering artifacts level and distribution. We found(More)
Level of artifacts in spectra obtained by Multidimensional Fourier Transform has been studied, considering randomly sampled signals of high dimensionality and long evolution times. It has been shown theoretically and experimentally, that this level is dependent on the number of time domain samples, but not on its relation to the number of points required in(More)
Random sampling of NMR signal, not limited by Nyquist Theorem, yields up to thousands-fold gain in the experiment time required to obtain desired spectral resolution. Discrete Fourier transform (DFT), that can be used for processing of randomly sampled datasets, provides rarely exploited possibility to introduce irregular frequency domain. Here we(More)
A new procedure for Fourier transform with respect to more than one time variable simultaneously is proposed for NMR data processing. In the case of two-dimensional transform the spectrum is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Therefore, it enables one to Fourier transform arbitrarily sampled(More)
The comprehensive description of Multidimensional Fourier Transform applied to arbitrary sampled NMR data is presented. Lineshapes and signal-to-artifact ratio are discussed in detail with regard to time domain sampling scheme and applied data weighting. It is demonstrated that transformation method with simple summation instead of numerical integration is(More)
Four novel 5D (HACA(N)CONH, HNCOCACB, (HACA)CON(CA)CONH, (H)NCO(NCA)CONH), and one 6D ((H)NCO(N)CACONH) NMR pulse sequences are proposed. The new experiments employ non-uniform sampling that enables achieving high resolution in indirectly detected dimensions. The experiments facilitate resonance assignment of intrinsically disordered proteins. The novel(More)
While NMR studies of proteins typically aim at structure, dynamics or interactions, resonance assignments represent in almost all cases the initial step of the analysis. With increasing complexity of the NMR spectra, for example due to decreasing extent of ordered structure, this task often becomes both difficult and time-consuming, and the recording of(More)
Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail.(More)
The development of non-uniform sampling (NUS) strategies permits to obtain high-dimensional spectra with increased resolution in significantly reduced experimental time. We extended a previously proposed signal separation algorithm (SSA) to process sparse four-dimensional NMR data. It is employed for two experiments carried out for a partially unstructured(More)