Aliasing, optimized

Movement to optimum by an inadequate linear model is also possible in cases when doing the mentioned eight trials is not acceptable. The values of linear regression coefficients are considerably above the values of those for interactions, the more so since linear effects are not aliased/confounded with interaction effects. Although the movement to optimum by an inadequate linear model is mathematically incorrect, it may be accepted in practice with an adequate risk. Note that when trying to optimize a process one should aspire towards both the smallest possible interaction effects and approximate or symmetrical linear coefficients. In problems of interpolation models, the situation is exactly the opposite since it insists on interaction effects, which may be significant. 

The fast FT allows optimal interpolation of data. The original N points are folded 0 to make 2N points and are then shifted by - - N (Figure 3). The fast FT then creates 2N points in the frequency domain, which are padded by the desired number of extra zeros in the appropriate location in the middle (e.g., 6N zeros in total for fourfold interpolation) and transformed back. (The extra zeros are added in the middle because of the aliasing of points from - Vmax to 0 into v ,ax to 2v ,ax 3S shown in Figure 3.) This procedure creates interpolated points between the original data points. 

A careful Doppler technique allows a better evaluation of all vascular structures involved (Bertolotto et al. 2003). Optimization of the color Doppler parameters to detect slow velocity flows allows evaluation of the penile vessels and eases identification of the color hlush from the torn artery. However, visualization of high velocity flows is not correct, and aliasing hampers visualization of the exact site of the cavernosal tear. When color Doppler velocity scale is increased, depiction of lower veloc-... 

B. Vitorge, D. Jeannerat, NMR diffusion measurements in complex mixtures using constant-time-HSQC-lDOSY and computer-optimized spectral aliasing for high resolution in the carbon dimension, Anal. Chem. 78 (2006) 5601-5606. 

D. Jeannerat, Computer optimized spectral aliasing in the indirect dimension of... 

Fig. 20 Selected PANACEA spectra of a cholesterol sample (ca. 30% in CDCI3) recorded on a Varian 600 MHz NMR system equipped with two receivers and a cryogenic HCN probe optimized for C-13 detection. The experiment time was 23 min. A fourfold undersampling (aliasing) was used with optimized offset and spectral window in the Fi (SQ) dimension, (a) Inadequate spectrum (b) multiplicity edited HSQC spectrum (the negative peaks are shown in red). Reproduced from Ref. 36. Elsevier, 2010...

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