Effect of apodization

Ong, W. Y., He, X., and Patel, S. C. (2006). Neuroprotective effect of apoD on hippocampal neurons after kainic acid-induced injury. J. Neurochem. 96(Suppl 1) 77... 

The acyltransferase activity of LCAT is dependent on the presence of apoA-I (A10, A16, A25, C15, F14, K15, Yl) or, probably to a lesser extent, on the presence of apoC-I (A16, S46). Kostner (K17) reported that apoA-III (thought by some to be apoD) is a cofactor for the LCAT reaction, whereas Albers et al. were unable to demonstrate any effect of apoD (or apoC-II, apoC-III, or apoA-II) on the reaction (A16). 

The effect of having a large solid angle is similar to the effect of apodization. For this reason, it has been called self-apodization [13]. 

The wavenumber resolution 8v of the measured terahertz spectmm is given as Sv 1 /L aY (see Section 4.4.1). For example, if the maximum optical path difference is 30 cm, the wavenumber resolution of the measured spectrum if about 0.03 cm . In practice, as a result of the effect of apodization, the wavenumber resolution may not be as high as this value, but in principle the relationship described in Sections 3.2.2 and 4.4.1 holds also in THz-TDS. 

Figure 3.10 Effect of different window functions (apodization functions) on the appearance of COSY plot (magnitude mode), (a) Sine-bell squared and (b) sine-bell. The spectrum is a portion of an unsymmetrized matrix of a H-COSY I.R experiment (400 MHz in CDCl, at 303 K) of vasicinone. (c) Shifted sine-bell squared with r/4. (d) Shifted sine-bell squared with w/8. (a) and (b) are virtually identical in the case of delayed COSY, whereas sine-bell squared multiplication gives noticeably better suppression of the stronger dispersion-mode components observed when no delay is used. A difference in the effective resolution in the two axes is apparent, with Fi having better resolution than F. The spectrum in (c) has a significant amount of dispersion-mode line shape.

Aminoanthracene, 1- and 2-, reactions, effects of ion source temperature, 185,187/ Analytical Fourier transform mass spectrometry, instrumentation and application examples, 81-98 Apodization, 27,28 Applications, future, 14,15 Aromatic amines, negative ion chemical ionization, 176... 

In order to compensate for ringing, a mathematical process known as apodization is used. This multiplies the collected data by a function that gradually approaches zero and has a value of 1 at the ZPD. Using apodization effectively reduces the ringing in the spectrum, but unfortunately, also the resolution decreases. Several algorithms have been established to eliminate the effects of ringing while maintaining as much resolution in the spectrum as possible. 

A(8) is called the boxcar function. This limit on the retardation leads to a limit on the resolution of 1/2L, so if L - 100 cm, the highest resolution attainable is 0.005 cm-1. By the convolution theorem, the product of two functions in one space is the same as the convolution of the Fourier transforms of the two functions in the reciprocal space. The effect of multiplying by this boxcar function is to convolve each point in the reciprocal wavenumber space with a sine function [sinc(x) = sin(x)/x Figure 4], An undesirable feature of the sine function as a lineshape is the large amplitude oscillation (the first minimum is -22% of the maximum). This ringing can make it difficult to get information about nearby peaks and leads to anomalous values for intensities. This ringing can be removed by the process known as apodization. 

But what does apodization mean for a continuous spectrum In a computer-simulated example (see Appdx) and where the ideal spectrum is known, the effect of the apodization is shown for two different values of Sm x (Fig. 11). Without apodization, the secondary extrema of the spectral window [see Fig. 6 and Eq. 

Now, let us consider phase errors. As already pointed out, an error arises when the true origin of the interferogram is missed by a small path difference b <. As (Fig. 40 a) where Js is the sampling interval. This error is called a linear phase error because 2nvB means an erroneous phase shift in the interferogram function, which is linear with respect to the wave number v. Including the effects of truncation and apodization, we obteiin for the cosine transform of the double-sided interferogram with a phase error e approximately ss.es.vo) ... 

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... 

An additional problem in FT deconvolution results from the finite number of data points. Back transformation frequently leads to wave-like curves, which cannot be attributed to real periodicities of the Fourier transform. To suppress these undesired side effects, an apodization function in the form of a triangular or parabolic function is applied. In analogy to Eq. (3.27), the decon-voluted signal is calculated by using an apodization function, Z)(v), by... 

Effect of the Finite Record Length Leakage and Apodization... 

Effect of the Finite Record Length Leakage and Apodization 47 Table 5.1. Coefficients of the Norton-Beer apodization functions. 

In previous sections, we examined several physically important noise-free signals. [We did briefly consider the effect of noise as a radiation source, but did not consider noise contributions to the observed response to an excitation.] In the absence of noise, a signal of any shape can be analyzed to determine its parameters (e.g., spectral line position, width, area, etc.). However, noise superimposed on a signal can obscure its information content, and it may therefore become desirable to sacrifice one kind of information (e.g., resolution) in order to improve the quality of other information (e.g., signal-to-noise ratio). When an already acquired signal is modified before Fourier transformation, the modification is called apodization (literally, "removal of feet", named after early efforts to smooth FT/IR line shapes—see de Haseth Chapter). 

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 ).

To reduce the side band-creating effect of truncation, the transient is normally subjected to apodization prior to FT. Apodization means the multiplication of the signal by a mathematical function that causes the values to smooth out to zero. Some sophisticated apodization methods are in use to deliver the ultimate resolution, nonetheless, single sin (x) or sin (x) functions work well. 

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