Zero-filling

13 Zero filling. To increase the digital resolution of the spectrum, the number of points can be increased before FT. The FID then consists of the acquired number 

With 2D WIN-NMR zero filling is defined simply by setting SI for the F2 and Fl dimension in the Parameters dialog box opened with the General parameters setup command in the Process pull-down menu prior to Fourier transformation. 

Try out the effect of zero-filling on the 1D C raw data of peracetylated glucose D. NMRDATA GLUCOSE 1 D C GC 001001. FID. 

Load the raw data of the gradient enhanced, double quantum filtered 2D 

The total number of points to be transformed after zero-filling usually presents little problem in terms of data storage or computational capacity of modern computers for a ID data set. However, as we shall see later, in 2D (and especially in 3D or 4D) NMR the approach outlined here that optimizes spectral width, resolution, and zero-filling independently often leads to data tables that are beyond the capacity of most computers to process in reasonable periods of time. In such cases, compromises must be made, as we discuss in later chapters. 

Without zero-filling, data points in the transformed spectrum occur only at multiples of 1/T Hz, which correspond to zero-crossings of the sine function, as shown in Fig. 3.8 hence the sidelobes are not observable. Doubling the number of points by zero-filling also places points only at zero-crossings for the absorption mode. Only when the number of points is quadrupled are the sidelobes observable. 

After the application of weighting functions (primarily in NMR), the next step in data processing is to zero fill the data to at least a factor of two (called one level of zero filling). The reason for this step is that the complex Fourier transform of np data points consists of a real part (from the cosine part of the FT) and an imaginary part (from the sine part of the FT), each containing np/2 points in the frequency domain. Therefore, the actual spectrum displayed is described by only half of the original number of points. The technique of zero 

Zero filling beyond a factor of two also can be done, but does not produce further improvement in line width. It is useful, however, in quantitative work (Section 2-6c), because it provides more data points to define line shapes and the positions of signals. 

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The effective resolution is determined by the number of data points in each domain, which in turn determines the length of t and <2- Thus, though digital resolution can be improved by zero-filling (Bartholdi and Ernst, 1973), the basic resolution, which determines the separation of close-lying multiplets and line widths of individual signals, vdll not be altered by zero-filling. 

In the case of the t domain, since it is only the number N of data points that determines the resolution, and not the time involved in the pulse sequence with various delays, it is advisable to acquire only half the theoretical number of FIDs and to obtain the required digital resolution by zero-filling. Thus the resolution in the Fi domain will be given by R = 2SWi/A i that in the F2 domain is given by / = 1/AQ = 2SW2/A2. 

Figure 3.5 Schematic representation of data processing in a 2D experiment (one zero-filling in and two zero-fillings in F ). (a) A(, FIDs composed of Afj quadrature data points, which are acquired with alternate (sequential) sampling, (b) On a real...

The sine-bell functions are attractive because, having only one adjustable parameter, they are simple to use. Moreover, they go to zero at the end of the time domain, which is important when zero-filling to avoid artifacts. Generally, the sine-bell squared and the pseudoecho window functions are the most suitable for eliminating dispersive tails in COSY spectra. 

Zero-filling A procedure used to improve the digital resolution of the transformed spectrum (e.g., in the tj domain of a 2D spectrum) by adding zeros to the FID so that the size of the data set is adjusted to a power of 2. Zero-quantum coherence The coherence between states with the same quantum number. It is not observable directly. 

Fig. 40.14. Effect of zero filling on the back transform of the pulse NMR signal given in Fig. 40.12. (a) before zero filling, (b) after zero filling.

Because the FFT algorithm requires the number of data points to be a power of 2, it follows that the signal in the time domain has to be extrapolated (e.g. by zero filling) or cut off to meet that requirement. This has consequences for the resolution in the frequency domain as this virtually expands or shortens the measurement time. 

Figure 14. Contour plot of the 360 MHz H-NMR correlation spectrum of dl-camphor. A 64 x256 data set was accumulated with quadrature phase detection in both dimensions and the data set was zero filled once in the dimension and symmetrized. T was 5 sec and t was incremented by 1.63 msec. Total accumulation time was 24 minutes and data workup and plotting took 15 min.

Figure 17. Contour plot of the 360MHz homonuclear spin correlation mpa of 10 (2 mg, CDCL, high-field expansion) with no delay inserted in the pulse sequence shown at the top of the figure. Assignments of cross peaks indicating coupled spins in the E-ring are shown with tljie dotted lines. The corresponding region of the one-dimensional H NMR spectra is provided on the abscissa. The 2-D correlation map is composed of 128 x 512 data point spectra, each composed of 16 transients. A 4-s delay was allowed between each pulse sequence (T ) and t was incremented by 554s. Data was acquired with quadrature phase detection in both dimensions, zero filled in the t dimension, and the final 256 x 256 data was symmetrized. Total time of the experiment was 2.31 h (17).

Because we are always in a hurry (so many samples, so little spectrometer time) we always try to acquire that little bit faster than we should. This is particularly true with 2-D acquisitions which can be very time-consuming. As discussed previously, we try to minimise the number of increments to save time. This gives rise to highly truncated data sets and poor resolution. This can be made to look a little prettier by adding a load of zeros to the experiment before Fourier transforming it. We call this (somewhat obviously) zero filling . Note that this doesn t add any information but it does make the result look nicer. 

Second, the resolution achieved in a 2-D experiment, particularly in the carbon domain is nowhere near as good as that in a 1-D spectrum. You might remember that we recommended a typical data matrix size of 2 k (proton) x 256 (carbon). There are two persuasive reasons for limiting the size of the data matrix you acquire - the time taken to acquire it and the shear size of the thing when you have acquired it This data is generally artificially enhanced by linear prediction and zero-filling, but even so, this is at best equivalent to 2 k in the carbon domain. This is in stark contrast to the 32 or even 64 k of data points that a 1-D 13C would typically be acquired into. For this reason, it is quite possible to encounter molecules with carbons that have very close chemical shifts which do not resolve in the 2-D spectra but will resolve in the 1-D spectrum. So the 1-D experiment still has its place. 

Zero filling Cosmetic improvement of a spectrum achieved by padding out the FID with zeros. 

Data shown as examples in this review were typically acquired as 2K X 128 or 2K x 160 point files. Data were processed with linear prediction or zero-filling prior to the first Fourier transform. Data were uniformly linear predicted to 512 points in the second dimension followed by zero-filling to afford final data matrices that were 2K x IK points. 

Figure 9 1,/i-ADEQUATE spectrum of strychnine (1) optimized for 5 Hz. The data were acquired using a sample of 1.8 mg in 40 j.Lof deuterochloroform in a 1.7-mm NMR tube at 600 MHz using a 1.7-mm Micro CryoProbe. The data were acquired as IK x 160 points with 320 transients/q increment and a 3-s interpulse delay giving an acquisition time of 48 h 17 min. The data were linear predicted to IK points in the first dimension and from 160 to 512 point in the second frequency domain followed by zero-filling to give a final IK x IK data matrix. 

After activation under vacuum, the cell was cooled by liquid nitrogen so that the sample reached the temperature of 100 K, and carbon monoxide (CO) was introduced progressively (7.5 pmol.g"1 at a time) into the cell. Spectra are recorded at room temperature on a Nicolet Magna 750 spectrometer, at an optical resolution of 4 cm 1, with one level zero filling in the Fourier transform (0.5 cm 1 data spacing) and normalized to 10 mg wafers. 

Fig. 13. 13Ca-1HN planes from the HN(CO)CANH-TROSY (a) and HN(CO)CA-TROSY (b) spectra. Spectra were recorded on uniformly 15N, 13C, 2H enriched, 30.4 kDa protein Cel6A at 800 MHz at 277 K. The data were measured using identical parameters and conditions, using 8 transients per FID, 48, 32, 704 complex points corresponding acquisition times of 8, 12, and 64 ms in tly t2, and <3, respectively. A total acquisition time was 24 h per spectrum. The data were zero-filled to 128 x 128 x 2048 points before Fourier transform and phase-shifted squared sine-bell window functions were applied in all three dimensions. 

K X 512 real data points with zero-filling applied in the dimension to 2 K data points. For eaeh inerement 16 or 32 FID s were aeeumulated with a relaxation delay of 2 s. 

A pre-requisite for the successful extraction of key NMR parameters from an experimental spectrum is the way it is processed after acquisition. The success criteria are low noise levels, good resolution and flat baseline. Clearly, there are also experimental expedients that can further these aims, but these are not the subject of this review per se. In choosing window functions prior to FT, the criteria of low noise levels and good resolution run counter to one another and the optimum is just that. Zero filling the free induction decay (FID) to the sum of the number acquired in both the u and v spectra (in quadrature detection) allow the most information to be extracted. 

Zero filling the FID more than a factor of two does not contribute to information extraction and any features revealed by this are artefacts. In most instances, zero filling by a factor of two amounts to an interpolation procedure benefiting primarily peak-picking. There are other procedures which can allow peak-picking interpolation between data points and the one used by the author is a simple equation to fit the maximum intensity and one point either side to a parabola and compute the position of its maximum. Bruker peak-pick table positions for instance are not separated by a multiple of the digital resolution and it would seem that they use the same or an analogous procedure. 

As described in Section 10.2, the final output from the NMR spectrometer to the computer is an FID. Typically 2048 096 digital points are accumulated in the FID and the next step is to improve the potential resolution of the FID by zero-filling the FID to 16384 digital points by adding zeroes to the end of the FID. Upon Fourier transformation (FT) the resultant spectrum contains 16384 points describing a spectral width of 2000-4000 Hz depending on the settings in the ADC. 

Fig. 4. Two-dimensional (2D) spectra of cyclo(Pro-Gly), 10 mM in 70/30 volume/volume DMSO/H2O mixture at CLio/27r = 500 MHz and T = 263 K. (A) TCX SY, t = 55 ms. (B) NOESY, Tm = 300 ms. (C) ROESY, = 300 ms, B, = 5 kHz. (D) T-ROESY, Tin = 300 ms, Bi = 10 kHz. Contours are plotted in the exponential mode with the increment of 1.41. Thus, a peak doubles its intensity every two contours. All spectra are recorded with 1024 data points, 8 scans per ti increment, 512 fi increments repetition time was 1.3 s and 90 = 8 ps 512x512 time domain data set was zero filled up to 1024 x 1024 data points, filtered by Lorentz to Gauss transformation in u>2 domain (GB = 0.03 LB = -3) and 80° skewed sin" in u), yielding a 2D Fourier transformation 1024 x 1024 data points real spectrum. (Continued on subsequent pages)...

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