Signal-noise separation

Signal-noise separation (SNS) by Froissart doublets within the FPT<+) and FPT( ) is illustrated in Figures 4.10 and 4.11 for the noise-free and noise-corrupted time signals, respectively. Only a small number of all the obtained Froissart doublets appears in the shown frequency window in Figure 4.10. The selected subinterval 0-6 ppm is important because all the MR-detectable brain metabolites lie within this chemical shift domain of the full Nyquist range. Froissart doublets as spurious resonances are detected by the confluence of poles and zeros in the list of the Pade-reconstructed spectral parameters. 

Dz. Belkic, Exact signal-noise separation by Froissart doublets in the fast Pade bansform for magnetic resonance spectroscopy, Adv. Quantum Chem. 56 (2009) 95. 

Dz. Belkic, K. Belkic, The general concept of signal-noise separation (SNS) Mathematical aspects and implementation in magnetic resonance spectroscopy, J. Math. Chem. 45 (2009) 563. 

D2. Belkin, K. Belkic, Pade-Froissart exact signal-noise separation in nuclear magnetic resonance spectroscopy, J. Phys. B At. Mol. Opt. Phys. 44 (2011) 125003. 

With regard to point (2) mentioned earlier, because of its linearity, the FFT imparts noise as unaltered from the time domain to the frequency domain. Moreover, the FFT has no possibility of separating noise from the true signal. In an attempt to improve resolution, one tries in vain to increase the total acquisition time, but for longer signals, noise becomes the major content to the encoded signals or free induction decay (FID) curves. 

A compromise between an optimized separation and a good detection without interferences and with sufficient signal/ noise ratio must be found. Often, separation or detection therefore occur in a non-... 

GI-XAS work at still lower energies (100-1000 eV) is also possible, allowing analysis of the edge spectra of C, N and O. For these energies bulk experiments are impractical unless extremely small nanoparticles and sample thickness can be prepared. GI-XAS experiments need to be done in chambers where control of water content and surface water layer thickness is possible. However detector resolution is insufficient at this time to separate incident beam energy and fluorescent photons so that a signal/noise problem limits sensitivity. 

The signals detected separately by a Fourier transform instrument and by a dispersion instrument remain the same as stated earlier. Now, however, for photon shot noise the noise level is proportional to the square root of the signal level.35-37 For the dispersion instrument, the signal-to-noise ratio in the spectral element d[Pg.436]

The aim of the selection and definition of chromatographic conditions is to achieve a proper separation of the components of the oil, both for the qualitative analysis, as also for the proper quantification. To do so, well resolved peaks and not distorted ones, good relation signal-noise and horizontal base line with absence of drift, must be obtained for each one of the components. 

In any use of separation techniques, most accurate knowledge of the chromatogram, the components included, and the basis line course should be available. What is the resolution between the peaks How is the baseline Is there is a baseline drift What is my signal/noise ratio What are the side component peaks relative to the maximum amplitude Which symmetry does each individual peak have ... 

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