Time-domain FID

Once the basic work has been done, the observed spectrum can be calculated in several different ways. If the problem is solved in tlie time domain, then the solution provides a list of transitions. Each transition is defined by four quantities the mtegrated intensity, the frequency at which it appears, the linewidth (or decay rate in the time domain) and the phase. From this list of parameters, either a spectrum or a time-domain FID can be calculated easily. The spectrum has the advantage that it can be directly compared to the experimental result. An FID can be subjected to some sort of apodization before Fourier transfomiation to the spectrum this allows additional line broadening to be added to the spectrum independent of the sumilation. 

The data on modern NMR spectrometers are obtained in the time domain (FIDs) i.e., they are collected and stored in the computer memory... 

The two dimensions of two-dimensional NMR spectroscopy are those of time. In one time domain, FIDs containing frequency and intensity information about the... 

Every NMR experiment must have a preparation sequence (inducing the nuclei to resonate) and detection capability (finding out what happened). Two-dimensional NMR spectroscopy adds two more domains between preparation and detection. These are an indirect evolution time, q, and a mixing sequence (see Figure 3.15). The two dimensions of two-dimensional NMR spectroscopy are those of time. In one time domain, FIDs containing frequency and intensity information about the observed nuclei is collected. The second time dimension refers to the time that elapses between some perturbation of the system and the onset of data collection in the time domain. The second time period is varied, and a series of FID responses are collected for each of the variations. 

After you Fourier transform your FID, you get a frequency-domain spectrum with peaks, but the shape of the peaks may not be what you expected. Some peaks may be upside down, whereas others may have a dispersive (half up-half down) lineshape (Fig. 3.36). The shape of the peak in the spectrum (+ or — absorptive, + or — dispersive) depends on the starting point of the sine function in the time-domain FID (0° or 180°, 90° or —90°). The starting point of a sinusoidal function is called its phase. Phase errors come in all possible angles, including those intermediate between absorptive and dispersive (Fig. 3.37). The spectrum has to be phase corrected ( phased ) after the Fourier transform to obtain the... 

The NMR information contained in the FID is a signal-time function that is not easily interpreted. Therefore, a mathematical operation (FT) is used to convert the time-domain FID(t) into the frequency-domain NMR spectrum, F(v) (Fig. 5.4.3b). 

Fig. 3 (A) Interaction of Mq with Bq and Bi fields (B) time domain FID and (C) frequency domain spectrum obtained from Fourier transformation of the FID.

Figure 2.18. Fourier transformation of time domain FIDs produces the corresponding frequency domain spectra.

FIGURE 20.6. (a) Representation of a 90° rf pulse (6i) and the ensuing Free-induction-decay (FID), (b) Fourier transformation of the time-domain FID into the frequency-domain signal. 

The kind of NMR data required (e.g. signal amplitudes, relaxation information or chemical shift information with limited spectral resolution) plays a significant role in defining the design criteria for both hardware and software components. In common practice, in low-resolution NMR the concern is with the analysis of the NMR signal in the time domain (FID) and the characterisation of the physical structure of the bulk sample. The global characterisation of the sample in terms of molecular dynamics is key to successful use of low-field NMR. Relaxation information should provide rapid, reliable quantitative information for improved process control. The relaxation behaviour can provide extremely useful information on various aspects of mobile phases, e.g. moisture determination. 

High quality paper, a bi-component material made of cellulose, bound water and (in)organic additives and impurities, has been characterised by CP-MAS NMR at 100 MHz, pulse H LR-NMR relaxation at 57 MHz, and ESR [221]. The time domain (FID) shows cellulose as a fast decaying component and water as the slowly decaying one in the frequency domain the cellulose component is broad while the water component, which is strongly bound to cellulose, is sharp (Fig. 7.13). The state of conservation of paper correlates with the amount of paramagnetic rhombic Fe impurities, as determined by ESR. 

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