Processing zero filling

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...

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. 

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. 

Later section.s of this chapter deal with more advanced and specialised processing options such as zero filling, linear prediction, deconvolution and the manipulation of 2D data sets. The chapter concludes with a set of tables containing recommendations for the type of processing function and the corresponding parameters to be used in a number of ID and 2D experiments. 

Prior to Fourier transformation the actual number of measured data points and the total number of data points to be transformed may be defined. With ID WIN-NMR the following definitions are valid and may be inspected for the actual data file by selecting the Zero Filling... option in the Process pull-down menu. 

There are three main processing options based on the addition of a processing or correction function to the FID DC- or Baseline-Correction, Zero-Filling and Linear Prediction LP. 

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. 

These options are available only with ID WIN-NMR via the FID Shift..., Adjust Point and Zero Filling... options in the Process pull-down menu. Use the Help tool for more information about these options, their dedicated panel buttons and how to use them. 

Selecting this option in the pull-down menu Process initiates an inverse Fourier transformation. The result of this operation is a FID. Inverse Fourier transformation is of use, if only the spectrum is available and if processing in the time domain (weighting, zero-filling,. .) needs to repeated to improve and optimize the spectrum. Inverse FT is onyl available with ID WIN-NMR. 

Before performing the FT, there are two things we can do to enhance the quality of the spectrum. First, the size of the data set can be artificially increased by adding zeroes to the end of the list of FID data. This process of zero filling has no effect on the peak positions, intensities, or linewidths of the spectrum, but it does increase the digital resolution (fewer hertz per data point) in the spectrum (Fig. 3.31). This can be useful to give better definition... 

Figure 14 Stopped-flow TOCSY CEC-NMR spectra of paracetamol glucuronide. Acquisition parameters number of 144 scans for each of 256 increments. Spectral width of 4716 Hz, number of points 4096. Processing parameters zero filled and multiplied by apodization function of 3 Hz in both dimensions. (From Ref. 52 reproduced with permission from The Royal Society of Chemistry.)...

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. 

It is always better to record more data points in F2 than to zero-fill this dimension afterwards during processing. 

NOESY was performed at 32 °C on a VXR-500 spectrometer operating at a proton frequency of 500 MHz. The protein was dissolved in 20 mM sodium phosphate, pH 7.5 (direct pH meter reading), 100 mM NaCl, 5 mM DTT in D2O. The protein concentration was 2 mM. The data was acquired in the hypercomplex mode with a mixing time of 150 ms (Jeener et al., 1979 Macura Ernst,1980). The spectral width was 7200 Hz in both dimensions. 2048 complex points in the t2 dimension and 256 complex points in the tl dimension were acquired. 96 transients were collected for each FID. Data processing was performed on a Sun Sparc 10 station using VNMR software from Varian. The time domain data were zero-filled once and multiplied by shifted sinebell or Gaussian functions before Fourier transformation in both dimensions. Chemical shifts were referenced to internal sodium 3-(trimethylsilyl)-propionate-2,2,3,3-d4. 

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... 

Like acquisition, data processing is performed differently in 2D, compared with ID, NMR experiments. The principal reason is that signal truncation is a much more serious problem in 2D than ID experiments. Zero filling also is used in 2D experiments, as is the relatively new technique of linear prediction. 

Whilst the NMR response decays throughout the FID, the noise component remains essentially constant and will eventually dominate the tail of the FID. At this point there is little advantage in continuing acquisition since this only adds noise to the final spectrum. Provided the FID has fallen to zero when acquisition stops, one can artificially improve the digital resolution by appending zeros to the end of the FID. This process is known as zero-filling and it interpolates these added data points in the frequency-domain and so enhances the definition of resonance lineshapes (Fig. 3.15). 

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