Fourier analysis, advantages

If, instead of the nonlocal Fourier analysis, one uses the local wavelet analysis to represent a quantum particle, the uncertainty relationships may change in form. On the other hand, this process has the advantage of containing the usual uncertainty relations when the size of the basic gaussian wavelet increases indefinitely. 

In principle, Fourier analysis does not suffer from these shortcomings. By calculating the amplitude ratios and the phase lags for a series of frequencies, an unlimited number of equations can be obtained for the calculation of the transport parameters. However, due to the interactions that take place between the transport parameters at low frequencies and to the amplification of the experimental errors that take place at high frequencies, the advantages of the Fourier analysis on the method of moments are quite limited. Boersma-Klein et al. [85] carried... 

These values again compare very well with all available quantal results for this reaction (3a), (5b), ( ). An advantage of using periodic orbits, rather than quaslperlodlc orbits. In the semlclasslcal quantization scheme Is that the Fourier analysis needed to compute the two frequencies Is essentially trivial. 

A comparison between Bayesian and Fourier analysis is provided by Kotyk et and Evilia et They both show that the Bayesian methods provide more precise frequency estimates and far more precise amplitude estimates than DFT and explain the difference. However, it should be said that the methods are so different in nature that comparison is more difficult than for other methods discussed in this paper. For example, by known Ti the Kotyk etal. mean that T2 has been included in the calculation as a matched exponential apodiza-tion. Vines et demonstrated the ability to mea.sure scalar couplings that are much smaller than linewidth in the case of spectra with favorable S/N ratio. The same authors took advantage of the ability of BPT to accurately measure linewidth to improve exchange parameters and gain in the precision and accuracy of thermodynamic properties.- ... 

In principle we could perform Fourier analysis to find the model parameters, but for reasons explained below, it is in fact advantageous to follow a different procedure that is geared towards our synthesis goals. For purposes of modifying pitch, it is useful to perform the analysis in a pitch synchronous manner and in fact one of the main advantages of sinusoidal modelling is that the accuracy of this does not have to be as high as that for PSOLA [420], [293], [520]. 

Fourier analysis offers the process of selfdeconvolution that is capable of resolving imder-lying peaks from broad overlapping bands. Fourier self-deconvolution has the advantage over derivati-zed spectra that there is no shift or averaging effect and the self-deconvoluted spectrum is directly comparable with the log/reciprocal wavelength scale. 

Another advantage of frequency response analysis is that one can identify the process transfer function with experimental data. With either a frequency response experiment or a pulse experiment with proper Fourier transform, one can construct the Bode plot using the open-loop transfer functions and use the plot as the basis for controller design.1... 

IR reflectance allows the in situ analysis of the electrode-electrolyte interface [8, 9], The Fourier transform variant adds to this technique the advantage of very fast data collection [10],... 

Better procedures for determining particle sizes from X-ray diffraction are based on line profile analysis with Fourier transform methods. The average size is obtained from the first derivative of the cosine coefficients and the distribution of particle sizes from the second derivative. When used in this way, XRD offers a fundamental advantage over electron microscopy, because it samples a much larger portion of the catalyst. The reader is referred to publications by Cohen and coworkers for more details and examples [4,10,11],... 

Fourier spectroscopy, 23 137 Fourier transformation, essential equations for, 14 226-227 Fourier transform (FT) infrared (ftir) analysis, 19 563-564, 813. See also Microscopy-ftir technique dichroism, in silicone network characterization, 22 569 instruments, 23 138 advantages of, 14 228 resolution for, 14 227 microscopy, 14 232... 

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