Step apodization

At the end of the 2D experiment, we will have acquired a set of N FIDs composed of quadrature data points, with N /2 points from channel A and points from channel B, acquired with sequential (alternate) sampling. How the data are processed is critical for a successful outcome. The data processing involves (a) dc (direct current) correction (performed automatically by the instrument software), (b) apodization (window multiplication) of the <2 time-domain data, (c) Fourier transformation and phase correction, (d) window multiplication of the t domain data and phase correction (unless it is a magnitude or a power-mode spectrum, in which case phase correction is not required), (e) complex Fourier transformation in Fu (f) coaddition of real and imaginary data (if phase-sensitive representation is required) to give a magnitude (M) or a power-mode (P) spectrum. Additional steps may be tilting, symmetrization, and calculation of projections. A schematic representation of the steps involved is presented in Fig. 3.5. 

The next step after apodization of the t time-domain data is Fourier transformation and phase correction. As a result of the Fourier transformations of the t2 time domain, a number of different spectra are generated. Each spectrum corresponds to the behavior of the nuclear spins during the corresponding evolution period, with one spectrum resulting from each t value. A set of spectra is thus obtained, with the rows of the matrix now containing Areal and A imaginary data points. These real and imagi-... 

All the processing steps in this section are intended to enhance the time domain data leading to the suppression of distortions or artefacts and an improvement in the overall spectral quality. The suitability of the methods can be estimated from the appearance of the FID in the main spectrum window of ID WIN-NMR as illustrated in the schematic FID shown in Fig. 3.6. The envelope of the exponentially decaying FID has a dc offset as it is not symmetrical about the zero line whilst the spectrum lineshape may be improved by either zero filling or apodization or possibly both. 

Fig. 3.6 Time domain processing steps - dc offset correction, zero filling and apodization.

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... 

Load the configuration file ch5215.cfg. Simulate nine 13C spectra numbers (User ch521 Name 5215a Exp No. 1 to 9) incrementing the pulse pi from lOd to 90d in lOd steps. Process the FIDs (zero filling Si(r+i) 64k, apodization EM, LB 2.0 [Hz]) and save the spectra after Fourier transformation. Display all spectra In ID WIN-NMR using the option... 

The next step will be to perform some modifications on the CLEAN algorithm by coding a DFM specific one, in order to include some FTS algorithms such as phase correction and apodization. Apodization requires a unique zero path difference (ZPD), and research would need to be performed to design tailored apodization filters for DFM data. 

Of course, this is really tantamount to apodizing with a step function, and unless the signal has already decayed to the noise level by the cutoff time, it will naturally introduce side-lobes about each peak. This spectral distortion can be alleviated by use of apodization functions of "intermediate smoothness," i.e., in between the discontinuous extreme of the sharp cutoff and the gentle extreme of the exponential decay. A typical example would be an envelope function in the shape of a quarter-cycle of a sine function, so phased that it reaches zero just at the end of the desired time region. (For further discussion of these and related points see Ref. 14-16). 

We measure Raman line positions in much the same way as we measure atomic line positions but omit the apodization step. To interpolate additional data points between those actually measured, we stretch the Raman line by zero-filling. The result of an eightfold stretch of the 802-cm" line is shown in Fig. 6C. A polynomial is fitted to the tip of the line. Finally, the location of the maximum of the polynomial function is found and mapped to the original dataset. 

Apodization is a mathematical procedure used to overcome the fact that a recorded inter-ferogram is truncated (i.e., does not extend to an infinite distance) and to ensure that the interferogram to be Fourier-transformed terminates smoothly without a step. An explanation of apodization is given in Section 4.4.1. In Figure 5.12 , a trapezoidal apodization function is shown overlaid with a measured interferogram to be weighted by this apodization function. 

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