Fourier transform method, data

Radiofrequency spectroscopy (NMR) was introduced in 1946 [158,159]. The development of the NMR method over the last 30 years has been characterised by evolution in magnet design and cryotechnology, the introduction of computer-based operating systems and pulsed Fourier transform methods, which permit the performance of new types of experiment that control production, acquisition and processing of the experimental data. New pulse sequences, double-resonance techniques and gradient spectroscopy allow different experiments and have opened up the area of multidimensional NMR and NMRI. 

This filtering preprocessing method can be used whenever the variables are expressed as a continuous physical property. One example is dispersive or Fourier-Transform spectral data, where the spectral variables refer to a continuous series of wavelength or wavenumber values. In these cases, derivatives can serve a dual purpose (I) they can remove baseline offset variations between samples, and (2) they can improve the resolution of overlapped spectral features. 

The spin-lattice relaxation times of essentially all the protons in vindoline, measured by a Fourier transform method, show values reflecting the degree of steric interaction with other protons. (276) A wealth of coupling constant data has been made available by first order analysis of the 300 MHz NMR spectrum of vindolinine [458]. (277) H NMR shifts for the metabolite of vindoline [459] (278) are shown on the structure. 

The application of Fourier transform methods to nuclear magnetic resonance experiments improved the signal-to-noise ratio and permitted extraction of data heretofore inaccessible. 

Because our research is focused on problems relevant to secondary structure of proteins in solution, this section will briefly review the recent developments in spectroscopic techniques applied to this problem. These techniques are considered low-resolution methods which provide global insight into the overall secondary structure of proteins without being able to establish the precise three-dimensional location of individual structural elements [707], Vibrational spectroscopy has played a pioneering role in studying the conformations of peptides, polypeptides, and proteins [702]. The advent of stable and powerful lasers has led to the development of Fourier transform methods which allows the use of powerful computational techniques for the analysis of spectral data [10,103,104], Laser... 

For NMR spectra, it is known that if s(t) is the free induction decay following a pulse, S((o) represents the slow passage spectrum. We shall also use the FT relationship in other ways—for example, for data processing (in Section 3.4) and for analyzing random molecular motions (in Chapter 8). We return to the use of pulse Fourier transform methods in Section 3.6. 

Characterization of controlled pore glasses by small angle X-ray scattering and evaluation of the scattering data by the indirect Fourier transformation method... 

Sharpening of 121Sb Mossbauer spectra can be achieved in some cases by Fourier-transform methods, and this approach has been tested on data for CoSb3 and Fe0.5Ni0.sSb3.705... 

Fourier Transform Method. Another method of data reduction is to take a fast Fourier transform (FFT) of the wave (10). As indicated in Figure 7, the Fourier transform of a damped sine wave with a single frequency is a single maximum in the frequency domain at the frequency of the oscillation. The amplitude (H) of the transformed data as a function of angular frequency ([Pg.344]

The Fourier transform method requires a minimum of 1024 data points to provide enough resolution to calculate the damping coefficient. The FFT of 1024 data points takes approximately a minute with the HP 9825B computer, so this constitutes a practical limit in resolution due to computer memory size and time considerations. So as not to introduce error, the damped oscillations... 

The modem methods of taking NMR spectra involve the use of very short radio frequency pulses (of variable duration from 1 to 200 ms) instead of a continuous signal as in older NMR. This requires full automation of the test, the Fourier transform analysis, data storage and multiple scan capability. With the scalar (low power, ca. 4 kHz) and dipolar (about 45 kHz) decoupling, magic angle spinning and cross polarization methods one can obtain spectra of solid samples with resolution similar to those known for liquids. The spectra provide precise information on the... 

In early work (8) we used infrared spectroscopy coupled with attenuated total reflection optics. This work was done before the availability of infrared equipment based on Fourier transform methods. Due to their relative speed these methods now permit in situ, real time measurements with a resolution of 1 sec or less (9), and continue to yield valuable data, particularly in the hands of the Battelle group in a series of studies dating from 1979 (10). In our early infrared work we had to be content to rinse and dry the surface before obtaining the infrared reflection spectrum Nevertheless the values of surface concentration were remarkably close to those determined more recently. Infrared studies of proteins suffer generally from the fact that the main features of protein spectra are similar for all proteins and therefore it is difficult to distinguish one from another. 

GPS combined with gravity measurements The geoid determination and the height transfer across the Belt can also be based on gravity measurements. In the area of concern gravimetric measurement on land and sea have been performed in the past. Based on this data the Danish Geodetic Institute has carried out computations by Least-Squares Collocation (LSC) and by Fast Fourier Transform Method (FFT). A geoid, computed by the LSC... 

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