Time domain data points

TDj, ti time domain data points TD, time domain pairs of data points SI2 and SIi, total data points in Fj and F, domains, respectively Hz/PTj and Hz/PT], digital resolution in F and F, (real) domains NS, number of acquired transients DS, number of dummy transients Tr, recycle time. 

Although at first glance all FIDs look similar, the shape of FIDs differs and depends on the sample amount, kind of experiment (ID, 2D), the nuclei detected ( H, C) and on acquisition parameters such as the length of the acquisition time, the spectral window and the number of time domain data points TD. Subsequent processing must take this into account and be tailored to these different shapes. 

Sets of truncated and non-truncated ID FIDs have been prepared to explore the advantage,s and limitations of LP in the following Check its. To speed up the calculations, the number of time domain data points and the number of resonance lines in the corresponding spectra have been deliberately reduced to a small number. Suitable 2D data sets have also been prepared for use with 2D WIN-NMR (see Table 5.3). 

A series of 2D HMBC experiments have been performed to demonstrate the benefits of LP with 2D data. Whereas the number of time domain data points in t2 (TD2) remains the same for each experiment, the number of time domain data points in 11 (TD1) and the number of scan.s (NS) has been varied according to Table 5.3. Thi.s allows a comparison of the results obtained with/without the application of LP on the basis of the same measuring times but different number of scans per increment (005001,006001, 007001)... 

In a regular ID FT NMR experiment, the signal-to-noise ratio for a single time domain data point can be very poor, but the Fourier transformation takes the signal energy of all data points and usually puts it into only a few narrow resonance lines. Similarly, in a 2D experiment a spectrum with poor S/N may be recorded for each q value, but the Fourier transformation with respect to q combines the signal energy of a particular resonance from all spectra obtained for different q values and concentrates it into a small number of narrow lines in the 2D spectrum. 

The number of time domain data points (TD) means that the time over which data are collected (termed the acquisition time (AQ)) is given by AQ = TD X DW. Digitisers are characterised by the number of bits (determining the dynamic range with which the... 

T2 relaxation processes mean that the information is not equally distributed throughout the time domain data. The T2 decay of the signal means that the contribution from the signal relative to the noise decreases as the time increases. Therefore weighting functions can be applied to the time domain data points in order to emphasise the parts of the FID where the signal preferentially resides. 

Fig. 5. Prostate biopsy. H MR spectra (8.5 T, 37°C), of human prostate biopsy specimens (a) cancer (Gleason s grade 3+3) (b) benign prostatic hyperplasia (BPH). MR spectra were collected with presaturation of the water signal. Acquisition parameters included number of scans, 256 or 640, sweep width 5000 Hz, delay 2.41 s, and time domain data points 4K. Reprinted from Cancer Research with permission from the American Association for Cancer Research.

The averaging of the neighbouring time-domain data points in Eq. (24) is equivalent to convolution with a rectangular function. The width of the rectangle corresponds to the number of points that are averaged. The... 

The acquisition time is defined by the digitisation rate (which is dictated by the spectral width and defines the sampling dwell time DW) and on how many data points are sampled in total. If the FID contains TD time-domain data points then ... 

Spectral width, acquisition time and time domain data points... 

The digital spectral resolution is defined by the number of time domain data points for a given spectral width and is directly proportional to the length of the acquisition... 

In Check it 3.2.1.1 the correct measurement of two sets of signals is demonstrated. In addition the effect of the number of time domain data points TD on the digital resolution using the same spectral width recorded at higher magnetic field strengths is illustrated. 

The basic processing steps for ID NMR data can also be applied to the processing of 2D NMR data with similar effects. Of particular importance for the processing of 2D data matrices are zero filling and apodization. Usually 2D experiments are recorded with a relatively small number of time domain data points TD2, compared with a ID experiment, and small number of increments TDl in order to minimize data acquisition times. Typical time domain values are 512, Ik or 2k words. Small values of TD2 and TDl and the correspondingly short acquisition times cause poor spectral resolution and... 

The parameters TD and TDl relate to the number of time domain data points in a data set. TD determines the number of data points used to acquire the data in a standard ID experiment or in the f2 dimension of a 2D experiment. TDl determines the number of data points in the f 1 dimension and describes... 

As it has been discussed in the literature, we also compare the performance of straight Fourier transformation FFT on the NUS synthetic four-line spectrum in Fig. 3. We used the schedules obtained with the best seed numbers as in Fig. 2a and leave the missing time domain data points at zero value. The traces presented in Fig. 3 show that the artifacts due to the sampling schedules and lack of reconstruction are severe and mask the small peaks. However, the intense line is readily observable. Thus, straight Fourier transformation may be an option if one is only concerned with very intense peaks, such as methyl resonances in a protein, and weak peaks are of little concern. This treatment of NUS data may be useful for a quick inspection of an NUS data set to find out whether an experiment has worked. However, it should be followed by a reconstruction effort to retrieve best the full information content of the NUS data. 

Linear prediction. A mathematical operation that generates new or replaces existing time domain data points with predicted ones. Linear prediction can add to the end of an array of digitized FID data points, can extend the number of t, time domain data points in a 2-D interferogram, or can replace the initial points in a digitized FID that may have been corrupted by pulse ringdown. 

The 300 MHz spectrum of pergolide mesylate (10 mg/mL) in dimethylsulfoxide-d6 (2.5 ppm) is shown in Figure 3. The spectrum was obtained on a Varian Unity spectrometer using die following instrumental parameters 5 mm jual probe spectral width, 4416 Hz 90 pulse 64K time-domain data points acquisition time, 7.421 seconds 100 scans and probe temperature, 35°C. The spectrum was provided with 0.1 Hz Lorentzian line broadening. 

The 300 MHz proton NMR spectrum of ( )-sotalol in CD3OD is described in Table n. The spectrum was obtained on a Bruker AM-300 spectrometer. Instrumental settings were time domain (data points),... 

Notice that in the calculation of the acquisition time, we need only consider half the total time-domain data points since now two points are sampled at the same time. 

For the physical applications described in subsequent Chapters, it is usual to sample a spectrometer (or interferometer) time-domain (or pathlength) signal, y(t), at N different times. Since each time-domain point represents a weighted sun of oscillations at all the frequencies in the detected range (e.g., we hear all the tones at once while an orchestra plays), we have now-familiar situation of N observables (N time-domain data points) related to N desired frequen-... 

Although the discrete cosine Fourier transform yields N calculated frequency-domain values for N measured time-domain data points, the second half of the cosine F.T. data is a mirror image of the first half, and thus gives no new information. The other half of the time-domain information is contained in the first N/2 frequency-domain values of the sine Fourier transform. [It is possible to put all the information into the cosine transform by first adding N... 

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