Exponential apodization

The FIDs simulated using NMR-SIM should always be processed using the zero filling and apodization parameters shown in Table 3.1. This table also lists the abbreviations used for these parameters in the Check its. Occasionally parameters different from the recommended values may be used in a Check it this is particularly true in simulations where the relaxation option is disabled, the values of the parameters are chosen to improve the spectrum appearance by minimizing line distortions. The Check it may contain the phrase "use zero filling and an apodization (EM, LB 2.0 Hz)" implying zero filling of SI(r+i) 2 TD and an exponential apodization with a LB factor of 2.0. 

Tiziani et al. reported an extensive study on the comparison of two weighting functions, sine-bell and sine-bell combined with exponential, and their effects on the 2D /-resolved spectrum resolution and reproducibility. Their tests with dog urine, fish liver extract and leukaemia cell extract samples indicated that combined use of sine-bell and exponential apodization resulted in a better resolution and reproducibility, which should be beneficial in quantitative studies. 

Figure 7. Effect of multiplying the signal of Figure 6 by an exponential apodizing filter function exp(-t/2r ).

Figure 12. Effect of time range on Fourier transform of a relaxing signal. Same as Figure 11 except filtered with an exponential apodization function exp(-t/2T ).

Figure 1.36 Various selected apodization window functions (a) an unweighted FID (b) linear apodization (c) increasing exponential multiplication (d) trapezoidal multiplication (e) decreasing exponential multiplication (f) convolution differ-...

Apodization (exponential multiplication) is used to improve the signal-to-noise ratio, and it does not affect the chemical shifts of the NMR signals. 

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. 

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. 

Greek). Some of the obvious functions to use for apodization are the linear ramp and the decreasing exponential (Cooper, 1977). The latter is about the gentlest form of such an operation. 

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). 

The FIDs were zero filled to 64K data points and apodized by a 1.0 Hz exponential line broadening before Fourier transformation. The resulting spectra were individually phased and baseline corrected using the Bruker TOPSPIN 1.3 software (Bruker Biospin Gmbh, Rheinstetten, Germany). All spectra were referenced to TSP-d4 at 0.000 ppm. 

Finally, it should be noted that the first term in the expression for the Fourier transform of a Lorentzian band (Eq. 10.7) is yApeak, which is directly proportional to the area of the band. This term is unaffected by either multiplication of the Fourier domain array by an exponentially increasing function or by an apodization function. Thus, the area of each band in the spectrum is unaffected by FSD. Provided that (y y ) > Av (i.e., provided that the bands are still Lorentzian), the peak height of each band is increased to ApeakY/(Y y0> their FWHH is reduced from y to (y — y ). 

---