Fourier transform processes

The SNIFTIRS approach. The acronym SNIFTIRS means Subtractively Normalized Interfacial Fourier Transform Infrared Spectroscopy. The basic concept of this method involves the fact that the raw data obtained directly from the Fourier Transform process contain components which are undesirable. Firstly, there is material in the solution which may have affected the spectrum. Secondly, unwanted information on certain material on the electrode (adsorbed water, for example) is best eliminated. 

For all of the cases considered earlier, a C(t) function is subjected to Fourier transformation to obtain a spectral lineshape function 1(G)), which then provides the essential ingredient for computing the net rate of photon absorption. In this Fourier transform process, the variable 0) is assumed to be the frequency of the electromagnetic field experienced by the molecules. The above considerations of Doppler shifting then leads one to realize that the correct functional form to use in converting C(t) to 1(G)) is ... 

This Fourier transform process was well known to Michelson and his peers but the computational difficulty of making the transformation prevented the application of this powerful interferometric technique to spectroscopy. An important advance was made with the discovery of the fast Fourier transform algorithm by Cooley and Tukey 29) which revived the field of spectroscopy using interferometers by allowing the calculation of the Fourier transform to be carried out rapidly. The fast Fourier transform (FFT) has been discussed in several places 30,31). The essence of the technique is the reduction in the number of computer multiplications and additions. The normal computer evaluation requires n(n — 1) additions and multiplications whereas the FFT method only requires (n logj n) additions and multiplications. If we have a 4096-point array to Fourier transform, it would require (4096) (4095) or 16.7 million multiplications. The FFT allows us to reduce this to... 

This process is carried out using a computer, subsequent to obtaining the two-dimensional signal, S(kx, ky). A pulse sequence for two-dimensional Fourier imaging is shown in Figure 6. An example of the two-dimensional Fourier transform process is shown for two circular objects in Figure 7. 

Having said that the Fourier transform process enables us to transform information in the time domain into equivalent information in the frequency domain and vice versa, we will now consider the NMR experiment in the time domain. NMR is possible because nuclei of many atoms possess magnetic moments and angular momenta. (Electrons possess moments... 

It is important to realize that this approximately linear dependence of the phase angle on the offset is an intrinsic property of the experiment and has nothing to do with other mechanisms which can give rise to phase shifts such as instrumental delays in filters or inappropriate choice of the time origin in the Fourier transform process. In fact, since all these effects are approximately linear in x, they are usually lumped together and treated as one effect. Since the choice of the time origin is arbitrary and is entirely under the experimenter s control, all contributions to such frequency dependent phase shifts can be cancelled by an appropriate choice of the time origin and this is done quite often in FT of very wide lines. 

The spectrophotometer monitors infrared absorbance in the sample cell by carrying out repetitive scans for the predetermined wavelength or frequency range at a scan rate of up to 20 scans s . Consecutive scans can be added prior to the Fourier transformation. The fast Fourier transform process is a mathematical treatment of the recorded data that converts time domain data into frequency domain spectra [19,20]. That is, the intensity values... 

L.J. Bao, J.Y. Mo and Z.Y. Tang, Combined Spline Wavelet and Fourier Transform Processing Analytical Chemistry Signal, Chemistry in Hong Kong, 2 (1998), 53-58. ( )... 

Kazimierczuk K, Zawadzka A, Kozminski W, Zhukov I (2006) Random sampling of evolution time space and Fourier transform processing. J Biomol NMR 36 157-168... 

Pulse Doppler Radar processing of a coherent train of pulses usually with uniform spacing. Older versions implemented by analog filters modern versions use fast Fourier transform or discrete Fourier transform processing. 

Interpolation is a process used for determining precise peak positions and obtaining detailed features in a spectrum by interpolating appropriate data between adjacent recorded points within a discrete spectrum obtained by a discrete Fourier transform. The process introduced here does not estimate values by statistical analysis using the least-squares method, and so on, but rather derives the spectrum which should have been observed, by supplementing the Fourier transform process which deals with a limited number of sampling data values. 

This function is termed a Lorentzian line shape and is the NMR spectral result for a single nuclear type. For actual chemical systems, a number of different nuclear types will be present, and the FID are quite complicated [6]. The Fourier transform process separates the different contributions and produces the proper spectrum in the frequency domain [7]. This is the pulsed NMR Fourier transform experiment. 

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