![]() In this paper we discuss the features of time-resolved NUS and give practical recommendations regarding the temporal resolution and use of the time pseudo-dimension to resolve the components. Recently, time-resolved non-uniform sampling (NUS) has been proposed as a straightforward solution to the problem. Unfortunately, they are usually too lengthy to be applied in time-resolved experiments performed to study mentioned changes in a series of spectral "snapshots". The multi-dimensional NMR techniques are especially effective in a case of samples containing many components. In particular, the analyzed mixtures can undergo changes caused by chemical reactions. ![]() Besides the most straightforward application to study a stable sample containing a single compound, NMR has been also used for the analysis of mixtures. ![]() Nuclear magnetic resonance (NMR) spectroscopy is a versatile tool for chemical analysis. Our results show that the LPMP algorithm outperforms other CS algorithms when applied to exponentially decaying signals. We also consider certain modification of the algorithm by introducing the allowed positions of the Lorentzian peaks' centers. Thus, we propose the name Lorentzian peak matching pursuit (LPMP). The algorithm is based on the fact that the NMR spectrum consists of Lorentzian peaks and matches a single Lorentzian peak in each of its iterations. In this paper, we introduce a modification of OMP motivated by nuclear magnetic resonance (NMR) application of CS. Thus, dedicated algorithms for solving particular problems have to be developed. However, the condition of the applicability of standard CS algorithms (e.g., orthogonal matching pursuit, OMP), i.e., the existence of the strictly sparse representation of a signal, is rarely met. Resonance as seen through the frame of QED.Ī group of signal reconstruction methods, referred to as compressed sensing (CS), has recently found a variety of applications in numerous branches of science and technology. On the Feynman propagator technique and by exploring the cross links between basicĪspects of ‘‘semi-classical magnetic resonance’’ and the same basic aspects of magnetic In magnetic resonance by focusing on the concept of virtual photon exchange based The present article attempts to develop such a unified view for electromagnetic interactions (QED) with those of classical electrodynamics commonly used in magnetic resonance. Unified view when comparing the concepts and methods of quantum electrodynamics Or for studies in magnetic resonance with microscopically small samples or very weak rfįields as well as for other applications that may seem exotic today, to ask how to gain a Within this theoretical framework, it appears worthwhile either for educational purposes, Although in many applications there are very good reasons to work Spin particles are submitted to quantum theory and the electromagnetic field is treatedĪs a classical field. The definitions for both are given below.Magnetic resonance often relies on a semi-classical picture in which the Obvious in the Laplace Domain (Note: if you haven't studied Laplace Transforms, you may skip this paragraph). The relationship between step function and impulse function is even more ![]() Important result is that the function has zero width and an area of one. Note: this derivation of an impulse function is not unique. We use the vertical axis to show the area. Since we can't show the height of the impulse on our graph, With an area of one this is the unit impulse and we represent it by The limit as T→0, we get a pulse of infinite height, zero width, but still Rectangular pulse with height 1/T (the slope of the line) and width T. If we take the derivative of our ramp function (lower left), we get a If we let T→0, we get a unit step function, It is zeroįor tT, and goes linearly from 0 to 1 as time goes from 0 to T. This is, at first hard to visualize but we can do so byĬonsider first the ramp function shown in the upper left. One of the more useful functions in the study of linear systems is the "unit impulseĪn ideal impulse function is a function that is zero everywhere but at the The Unit Impulse Function Contents Time Domain Description
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