Line shape phase-twisted

Equation 3 indicates that the peaks in the two-dimensional spectrum may be positive or native, depending on their relative connectivities in the spin-spin coupling energy levels. Normally this information is lost as it is most convenient to display the data set in the absolute-value mode (Freeman and Morris, 1979). The phase correction for a two-dimensional data set is considerably more complicated than with one-dimensional data. Even when the cumbersome phase correction is carried out, the resulting line shape is twisted, making distinction of overlapping peaks diificult (Boden-hausen et al, 1977). Therefore, the D(Fi,Fi) data set is stored as absolute-value spectra. In order to obtain the most satisfactory line shapes, the free induction decays are often apodized with a sine-bell (DeMarco and Wuthrich, 1976) function, although other apodization functions may be used (Bax, 1982). 

The phase-twisted peak shapes (or mixed absorption-dispersion peak shape) is shown in Fig. 3.9. Such peak shapes arise by the overlapping of the absorptive and dispersive contributions in the peak. The center of the peak contains mainly the absorptive component, while as we move away from the center there is an increasing dispersive component. Such mixed phases in peaks reduce the signal-to-noise ratio complicated interference effects can arise when such lines lie close to one another. Overlap between positive regions of two different peaks can mutually reinforce the lines (constructive interference), while overlap between positive and negative lobes can mutually cancel the signals in the region of overlap (destructive interference). 

There are generally three types of peaks pure 2D absorption peaks, pure negative 2D dispersion peaks, and phase-twisted absorption-dispersion peaks. Since the prime purpose of apodization is to enhance resolution and optimize sensitivity, it is necessary to know the peak shape on which apodization is planned. For example, absorption-mode lines, which display protruding ridges from top to bottom, can be dealt with by applying Lorentz-Gauss window functions, while phase-twisted absorption-dispersion peaks will need some special apodization operations, such as muliplication by sine-bell or phase-shifted sine-bell functions. 

Peaks in homonuclear 2D /-resolved spectra have a phase-twisted line shape with equal 2D absorptive and dispersive contributions. If a 45° projection is performed on them, the overlap of positive and negative contributions will mutually cancel and the peaks will disappear. The spectra are therefore presented in the absolute-value mode. 

Equation 10.9 represents a complicated line shape, which is a mixture of absorptive and dispersive contributions. Figure 10.11 gives an example of such a phase-twisted line shape. The broad base of the line, caused by the dispersive contribution, and the difficulty in correctly phasing such a resonance make it unattractive for practical use. The phase twist problem can be alleviated by displaying only the absolute value mode... 

This simple phase-incrementation idea, not particularly emphasized by the authors at the time, has more recently had a considerable impact on NMR methodology. First, it was made the basis of one of the standard methods for obtaining pure-phase two-dimensional spectra, replacing the undesirable phase-twist line shape with a pure absorption-mode signal. Secondly, it has provided a neat way to generate an extensive array of simultaneous soft radiofrequency pulses covering an... 

Figure 5.21. A stacked plot illustration of (a) the phase-twisted line shape and (b) the double-absorption lineshape. Clearly the resolution in (b) is far superior and for this reason phase-sensitive methods are preferred.

Sometimes absolute value mode, as opposed to pure phase spectra, can be preferable for easy assignment, despite the theoretical disadvantages of a phase-twist line shape. Carbohydrate line widths are generally narrower than those of proteins and nucleic acids, and the use of absolute value spectra... 

The idea was to construct the mask similar to an undesired shape observed in the spectra, and use CLEAN to replace distorted peaks with those of a perfect Lorentzian shape. Shaka and co-workers [88] showed that the algorithm is able to convert a twisted shape to a double-absorption in 2D phase-sensitive J spectra of complex organic molecules. This was achieved by (1) locating the twisted-shape peaks, (2) simulating double-dispersion signals of the same line width at the same frequency coordinates, and (3) subtraction of the latter from the original spectmm. Effectively, the most intense peaks were in double-absorption while those ignored by CLEAN remained in the twisted shape. 

The simplest microwave circuit element is a uniform section of transmission line which can be used to introduce a time delay or a frequency-dependent phase shift. Other Hne segments for interconnections include bends, corners, twists, and transitions between lines of different dimensions. (See Fig. 4.22.) The dimensions and shapes are designed to minimize reflections and so maximize return loss and minimize insertion loss. 

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