Weight function rectangular

This equation holds strictly only for the apodization function A(5) = 1. However, the interferogram can only be recorded over a finite interval, from — max to -l- max, and not beyond these limits. The function A((5) is introduced and set equal to one for 1 1 < Vax and equal to zero for 1 > Vax-The reconstructed spectrum is, therefore, not the true spectrum but the convolution of the true spectrum with the Fourier transform of the rectangular weighting function A(<5). The Fourier transform of the... 

We note that the coordinate X directly reflects the distance between atoms one and two, whereas the coordinate X2 reflects a combination of both distances. Therefore, a knowledge of the two coordinates does not directly tell us what the distances are between the involved atoms. Also, for the potential energy function in a collinear collision, the natural variables will be the distances between atoms A and B and atoms B and C. These variables appear as the components along a new set of coordinate axes, if instead of a rectangular coordinate system we use a mass-weighted skewed angle coordinate system. 

Numerically the convolution of a step scan is merely the application of a sliding weighted mean (e.g. like the Savitzky-Golay method). The Fourier transform of the rectangular function has the shape of sin(nv)/(nv) (whereby n is inversely proportional to the width of the rectangle) and unfortunately approaches 0 only very slowly. To make do with a small number of points for a convolution, one must tolerate a compromise and renounce the ideal rectangular shape of the low pass filter (in the frequency domain). 

A variety of functions can be used for h(i) the choice is somewhat arbitrary. A function that weights channel x more heavily than channel x + i is generally desirable. However, the rectangular correlator... 

Therefore, we discuss the effect of LMCT in a different perspective. There are some difficulties for extracting LMCT effects from the Cl wave functions or the TDMs. Firstly, the evaluation of the weights of LMCT mixing in Cl wave functions is difficult because most virtual MOs contained in CSFs are delocalized between Ln and X. Secondly, the amount of mixing of LMCT CSFs is too small to analyze because the weight of the reference 4f CSFs exceeds 95 percent. Therefore, to remove the dominant 4f components, we focus on the Nocc x (Nact + Nya) rectangular block of transition density matrix elements, where Nocc, act. and T/vk are the numbers of the doubly occupied MOs, active MOs (4f), and virtual MOs, respectively. This rectangular block... 

The next problem is which function Z, Y, M, or e to fit. The answer is that it is most sensible from a statistical point of view to fit the data in measured rather than transformed form. Suppose that Z is measured in rectangular form. When both Z and the associated Y = Z data are separately fitted with P weighting, it is found that there are often significant differences between the parameter estimates obtained from the two fits. This is not unexpected the operation of taking an inverse (complex or not) on data with errors generally introduces a bias in the fitted results it is for this reason that the directly measured results should be fitted directly. 

Different approaches were studied for obtaining both water sorption coefficient and water permeability coefficient. For that, some authors cut rectangular specimens of polymer films which are dried in vacuum oven at 50°C and their weight was measured until reaching no weight loss change. The films were immersed in a deionized water bath at 37°C. All specimens were weighed as a function of immersion time until the sorption process was complete. Then, the mass uptake at time t, and water solubility were calculated and thereafter water diffusivity, sorption and permeability coefficients. 

Kerr-effect rise (step-on) and decay (step-off) transients for a rectangular pulse in E(t). Rosato and Williams (87-88) have deduced expressions for the rise and decay functions for the Kerr-effect and for dielectric relaxation for the more general case of a body undergoing reorientational motions (as for equation (19)). They show for a molecule having 2v symmetry that the Kerr-effect decay for the induced part is a weighted sum of correlation functions [Pg.259]

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