Free induction decay Fourier transformation

Faraday constant flavin adenine dinucleotide face-centred cubic free induction decay Fourier transform... 

Before the advent of Fourier transform spectrometers, wide-line NMR was done by sweeping the magnetic field and observing the dispersion signal, or by pulsing the radiofrequency and observing the free Induction decay without transformation. The very broad spectral widths have caused problems with baselines and faithful representations of the entire llneshapes. Various techniques, such as the quadrupole echo (lA), progressive phase alternation of the excitation pulse and detector, short spectrometer dead times, and post-acquisition spectral correction (15) have circumvented most of these. 

FID Free induction decay, decay of the induction (transverse magnetisation) back to equilibrium (transverse magnetisation zero) due to spin-spin relaxation, following excitation of a nuclear spin by a radio frequency pulse, in a way which is free from the influence of the radiofrequency field this signal (time-domain) is Fourier-transformed to the FT NMR spectrum (frequency domain)... 

Figure 1.26 Free induction decay and corresponding frequency-domain signals after Fourier transformations, (a) Short-duration FIDs result in broader peaks in the frequency domain, (b) Long-duration FIDs yield sharp signals in the frequency domain.

Although the idea of generating 2D correlation spectra was introduced several decades ago in the field of NMR [1008], extension to other areas of spectroscopy has been slow. This is essentially on account of the time-scale. Characteristic times associated with typical molecular vibrations probed by IR are of the order of picoseconds, which is many orders of magnitude shorter than the relaxation times in NMR. Consequently, the standard approach used successfully in 2D NMR, i.e. multiple-pulse excitations of a system, followed by detection and subsequent double Fourier transformation of a series of free-induction decay signals [1009], is not readily applicable to conventional IR experiments. A very different experimental approach is therefore required. The approach for generation of 2D IR spectra defined by two independent wavenumbers is based on the detection of various relaxation processes, which are much slower than vibrational relaxations but are closely associated with molecular-scale phenomena. These slower relaxation processes can be studied with a conventional... 

The signal (FID, free induction decay) resulting from an NMR experiment contains the original data which are stored in the computer, and after the Fourier transformation (FT) we obtain the NMR spectrum itself. 

Fourier Transformation. Mathematical process of converting the interference free induction decay into a spectrum. 

Free Induction Decay (FID) Interference pattern of decaying cosine waves collected by Fourier Transform spectrometers, stored digitally prior to Fourier Transformation. 

This effect induces a free induction decay (FID) signal in the detection circuit. The FID can be measured, and the normal absorption spectrum can be obtained by means of an inverse Fourier transform. A variety of experimental extensions have been developed for this approach. By means of particular pulse sequences it is possible to detect spin resonances selectively on the basis of a broad ensemble of properties such as spatial proximity and dipolar coupling strengths. The central fundamental quantity of interest is, however, still the energy spectrum of the nuclear spin,... 

Fig. 10.1. The top panel shows the free induction decay (FID) acquired for a sample of strychnine (1) at an observation frequency of 500 MHz. The spectrum was digitized with 16 K points and an acquisition time of 2 s. Fourier transforming the data from the time domain to the frequency domain yields the spectrum of strychnine presented as intensity versus frequency shown in the bottom panel.

Fig. 1. Top Scheme of an inversion recovery experiment 5rielding the longitudinal relaxation time (inversion is achieved by mean of the (re) radiofrequency (rf) pulse, schematized by a filled vertical rectangle). Free induction decays (fid represented by a damped sine function) resulting from the (x/2) read pulse are subjected to a Fourier transform and lead to a series of spectra corresponding to the different t values (evolution period). Spectra are generally displayed with a shift between two consecutive values of t. The analysis of the amplitude evaluation of each peak from — Mq to Mq provides an accurate evaluation of T. Bottom the example concerns carbon-13 Tl of irans-crotonaldehyde with the following values (from left to right) 20.5 s, 19.8 s, 23.3 s, and 19.3 s.

The corrected free induction decay Sc t) will transform to a spectrum Sc i ) in which not only the acetone signal but also all the ethanol signals have had the instrumental contributions to their lineshapes removed. Provided that the reference region lui to wr gives a complete and accurate representation of the experimental acetone lineshape, our deconvolution process should allow us to obtain a clean corrected spectrum even when the shimming is far from ideal. There are of course limitations on this process. If the experimental lineshape is very broad, it will clearly not be possible to obtain a corrected spectrum in which the lines are very narrow without some sort of penalty. Here the limiting factor is signal-to-noise ratio since S u>) is much sharper than Se u>), the ratio of their inverse Fourier... 

The way to ensure a clean extraction of an experimental reference signal is thus to zero-fill the experimental free induction decay s it) once before Fourier transformation, zero completely the imaginary part of the resultant spectmm, and zero all but the reference region to wr of the real part [7], Inverse Fourier transformation then gives a symmetric time-domain signal, the first half of which is the required experimental reference signal Sr t) ... 

The laser heating technique can be applied to perform temperature jumps by irradiating short laser pulses at the sample container. Ernst et al. (54) used such a temperature jump protocol to perform stop-and-go experiments. After the start of the laser pulse, the temperature inside the sample volume is raised to the reaction temperature, the conversion of the adsorbed reactants proceeds, and the H MAS NMR measurement is performed. After the laser pulse is stopped, the temperature inside the sample volume decreases to ambient temperature, and the C MAS NMR measurement is made. Subsequently, the next laser pulse is started and, in this way, the reaction is recorded as a function of the reaction time. By use of the free-induction decay and the reaction time as time domains and respectively, a two-dimensional Fourier transformation leads to a two-dimensional spectrum, which contains the NMR spectrum in the Ej-dimension and the reaction rate information in the Ts-dimension (54,55). 

H2OS3(CO)io. Figure 5 presents a proton NMR absorption spectrum for H2Os3(CO)io that was obtained by Fourier transformation of the free induction decay. The spectrum was taken at room temperature, but no difference was... 

Obviously, it is difficult to find a schematic representation for a compound absorbing 10 different frequencies. In such a case, M0 can be dissociated into many vectors, each of which precesses around the field with its own frequency (Fig. 9.7 shows a simplified situation). As the system returns to equilibrium, which can take several seconds, the instrument records a complex signal due to the combination of the different frequencies present, and the intensity of the signal decays exponentially with time (Fig. 9.9). This damped interferogram, called free induction decay (FID), contains at each instant information on the frequencies of the nuclei that have attained resonance. Using Fourier transform, this signal can be transformed from the time domain into the frequency domain to give the classical spectrum. 

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