Exponential window

Figure 9 Treating internal dynamics during the refinement process. Due to dynamics and the weighting of the NOE, the measured distance may appear much shorter than the average distance. This can be accounted for by using ensemble refinement techniques. In contrast to standard refinement, an average distance is calculated over an ensemble of C structures (ensemble refinement) or a trajectory (time-averaged refinement). The time-averaged distance is defined with an exponential window over the trajectory. T is the total length over the trajectory, t is the time, and x is a relaxation time characterizing the width of the exponential window.

Fig. 7. Comparison of the effects of sinebell and exponential windows used for preparation of power-mode and half absorption-mode spectra. The sample utilized was a polyether antibiotic portmicin [15] (20 mg), which was dissolved in 0.4 ml of CeDa.

Use the same series of data and follow the same procedure as before to try out the Lorentz-Gauss convert window type. There is one single parameter LB available to adjust the window. Set the initial value to LB = 0, increment and decrement its value in small steps and inspect the shape of the window using the interactive mode. Note that for LB > 0 the shape of the window is similar to the exponential window (signal-to-noise improvement) whereas for LB < 0 the window shape is similar to the sine-bell squared window. Try out a few values to enhance the signal-to-noise ratio and to improve the resolution, store the results and compare the spectra using the multiple display. 

Usually, the FID is Fourier transformed after the application of an exponential window function (25). The line-broadening factor is selected to provide a good S/N. As a rule, the line broadening is selected according to the width of a narrow singlet resonance - in H NMR normally to a value from 0.1 to 0.5 Hz (cf. Figures 2 and 3). The resolution of the spectrum may be enhanced, though with reduced sensitivity, if the FID is multiplied, for example, by... 

Bruker uses the command EM (exponential multiplication) to implement the exponential window function, so a typical processing sequence on the Bruker is EM followed by FT or simply EE (EF = EM + FT). Varian uses the general command wft (weighted Fourier transform) and allows you to set any of a number of weighting functions (lb for exponential multiplication, sb for sine bell, gf for Gaussian function, etc.). Executing wft applies the window function to the FID and then transforms it. 

Load the configuration file ch3221.cfg (File I Experiment Setup Load from file...)- Open the NMR-Sim settings dialog box (Options I NMR-Sim settings...) and select the option Relaxation Acquisition. Run the simulation (Go I Run experiment). Apply an exponential window function (Window button) but no DC correction. Fourier transform the FID (FT button). (The effects of window functions are explained in section 3.2.3). Save the spectrum (FilelSave) for comparison with the second calculation. For the second simulation select the option Relaxation None and run the simulation saving the file with a new name. Process the data in exactly the same way as for the first simulation (Window and then the FT button) and compare the two spectra using the dual display mode of 1D WIN-NMR (DisplayIDual Display) (see section 3.2.3.4). 

Apodization is the process of multiplying the FID prior to Fourier transformation by a mathematical function. The type of mathematical or window function applied depends upon the enhancement required the signal-to-noise ratio in a spectrum can be improved by applying an exponential window function to a noisy FID whilst the resolution can be improved by reducing the signal linewidth using a Lorentz-Gauss function. ID WIN-NMR has a variety of window functions, abbreviated to wdw function, such as exponential (EM), shifted sine-bell (SINE) and sine-bell squared (QSINE). Each window function has its own particular parameters associated with it LB for EM function, SSB for sine functions etc. 

The spin system file should contain six molecule statements, each starting with the command molecule and concluding with the command endmol as shown in the result file. The approximate natural abundance of each isotopomer should be added to the same line as the molecule command. Start the simulation using the Go I Run Experiment command. In ID WIN-NMR process the FID using zero filling of Sl(r+i) 32k and an exponential window function with a LB value of 1.0 Hz. 

Load the configuration file dsweep.cfg. Open the spin system file (Edit Spin system...) and note the spin system variable definition. Examine the pulse sequence (Edit Pulse program...) and note the additional loop command to increment the chemical shift. Using the GolRun Experiment command simulate the spectrum which corresponds to the excitation profile of a 90° TOPHAT pulse. In 1D WIN-NMR process the FID using zero filling of Sl(r+i) 32/cand an exponential window function with a LB value of 2 Hz. 

Load the configuration fiie stanih.cfg using the File I Experiment Setup I Load from file... command and replace the spin system either by the file examl.ham previously created in Check it 4.1.1.2 or the file examip.ham delivered with the program. Load the puise program ppexamS.seq and start the simuiation by the command Go I Run Experiment. In ID WIN-NMR process the FID using zero filiing of Sl(r+i) = 32k and an exponential window function with a LB vaiue of 1 Hz. The spectrum should be identical to the one displayed in Check it 4.1.1.2. 

Figure 19 Effect of a single decreasing exponential window function, exp(—Kt) (a) k = 1 Hz (b) k = 5 Hz. Note the poorer peak resolution and improved signal-to-noise in (b). These spectra depict the carbonyl region of poly(isobutyl methacrylate) in CDCI3 the x axes are in ppm. 

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