Two-dimensional data set

With the wealth of infonnation contained in such two-dimensional data sets and with the continued improvements in technology, the Raman echo and quasi-echo techniques will be the basis for much activity and will undoubtedly provide very exciting new insights into condensed phase dynamics in simple molecular materials to systems of biological interest. 

The two-dimensional data set S tu t ) requires two Fourier transformation operations. Explain why the time variable is almost always Fourier transformed before I]. 

The PCA results will change if the origin of the data matrix is changed. Figure 3.6 shows this effect for a two-dimensional data set. In the left picture the original data... 

As shown in Fig. 22, the resulting procedure, referred to as a multi-block experiment, produces a two-dimensional data set, such as an array of FIDs (its exact nature depends upon the signal acquisition method). The data of each x-block are then reduced to a single quantity, S(t) which should be proportional either to the total sample magnetization Ma(x) or to one of its components. Since the vertical scale of the relaxation curve is irrelevant, we can identify S(t) with Ma(x) at the exact time of detection (usually just after the first excitation pulse). 

In 2D NMR spectroscopy, a two-dimensional data set is acquired as a function of two time variables tx and t2 as shown schematically in Figure 14.4 [1, 7]. Figure 14.4a shows the general case while the three pulse sequence of Figure 14.4b represents a typical example. 

FIGURE 13.2. Principal component analysis definition of PCI and PC2 for a two-dimensional data set. 

Figure 5.7. A generalised scheme for the collection of a two dimensional data set. The experiment is repeated many times with the t -period incremented at each stage and the resulting FIDs stored separately. Following double Fourier transformation with respect to first t2 and then ti, the two-dimensional spectrum results.

This section introduces the most important experimental aspects relating to two-dimensional data sets, and again uses the COSY experiment to illustrate... 

Figure 5.25. The typical scheme followed in the processing of a two-dimensional data set. The items shown to the right are additional or alternative procedures that may be executed.

One might think that the one dimensional data from each run in a TS-PFR experiment should be filtered using one of the above methods and that would clean up the pertinent errors. This is not so. The data arising from a set of runs in a TS-PFR experiment need to be treated as a two-dimensional data-set, since in order to extract reaction rates it is necessary to find slopes between points from different runs. What needs to be done in this case is the following data from the whole TS-PFR experiment must be assembled into a kinetic surface and the surface smoothed as a whole. Slopes taken from this surface, in specific directions, are the rates of reaction. 

The same data analysis that is applied to the MS based chemical sensor data can also be used to examine traditional GC/MS data. This is accomplished by using special macros that create the samples mass fingerprints by adding the all the scans present in the total ion chromatogram (TIC). The resulting two-dimensional data set can be analyzed with multivariate software. 

This section introduces the most important experimental aspects relating to two-dimensional data sets and again uses the COSY experiment to illustrate these. Many of the discussions are simply extensions of what has already been discussed in Chapter 3 for the ID experiment and familiarity with this is assumed. No new concepts are introduced here, although a modified approach to experimental set-up and to data processing is essential if 2D experiments ate to he successful. 

Pixel Contraction of picture element. This term is used to refer to the definable resolution element of a two-dimensional data set, e.g., an image. 

Mechanical Steering. The simplest method of beam steering is to use a mechanism to reorient a transducer (usually a circular aperture) to a predetermined set of orientations so as to capture the required two-dimensional data set. This approach was dominant at first however, in the last 15 years, electronically steered systems have become, by far, the most popular. Mechanical systems usually use either a single-element transducer or an annular array transducer (Fig. 25.8). Tlie former will have a fixed focus while the latter does allow the focal point to be moved electronically. This will be discussed more fiilly later. 

FIGURE 4 Classic (black dashed lines) and robust (red solid lines) PCs for a simulated two-dimensional data set containing 151 samples. 

FIGURE 5 Projection of a simulated two-dimensional data set containing 13 samples onto a sphere of unit radius when the centre is at LI-median (red bullets are the samples projected). 

D. Graphic Display of the Two-Dimensional Data Set Applications of Two-Dimensional Spectroscopy to NMR... 

A two-dimensional data set is one that is collected as a function of two independent time periods ... 

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