Fourier transformation free induction decay curves

Transverse relaxation is caused by the distribution and fluctuation of the resonance frequency of the A spins. The distribution-induced relaxation is called free induction decay. The free induction decay curve is the Fourier transform of the spectral shape of the A spins. This spectral shape depends on the intensity and the pulse width of the incident microwave, when the total width of ESR spectrum is large as is the case for radical species in solids. Therefore, the analysis of the free induction decay curve gives no information on the nature of radical species in solids unless the pulse width is narrow enough to cover the entire ESR spectrum. 

The NMR signal obtained from the resonating nuclei after the sample has been irradiated by the pulse is the so-called free-induction decay curve. This curve consists of peaks and valleys. The spectrometer samples the free-induction decay curve at set time intervals and records the data, which are in a time domain. NMR spectra, however, are normally given in terms of frequency and therefore the spectrum must be transformed by use of the Fourier transform pairs ... 

FIGURE 213 Examples of FID (free induction decay) curves, prior to perfonning FT (Fourier transform) to get the corresponding spectra shown on the right of each set [37]. Fast acquisition of FID s is important, the shape of which carries the encoded frequencies and amplitudes of the components of the reaction mixture. 

Fig. 2. (a) The free induction decay, G(t) for 19F in a single crystal of CaFi for B0 along [1,0,0]. The experimental points are given by circles and crosses from the CW and pulse measurements, respectively, and the theoretical curve is that of Eq. (14), corresponding to an exponential decay multiplied by a sine function. Note that F(t) is equivalent to G(t) in the present notation. Reproduced with permission from A. Abragam, The Principles of Nuclear Magnetism, p. 121, Oxford University Press, London, 1961. (b) The lineshape in the frequency domain corresponding to the Fourier transform of the theoretical curve. 

Fourier Transform NMR. In Fourier transform NMR (FTNMR), a repetitive radio frequency (RF) pulse is applied in order to excite all of the nuclei of the particular nuclear species being studied. The sum of the free induction decay (FID) curves from each pulse is analyzed by a Fourier transform method in order to generate the familiar frequency domain spectra. Fundamentally, parameters such as the frequency, intensity, application time of the appropriate RF pulse, and time intervals between these pulses are important variables when using this technique. The principle of the pulsed Fourier transform technique can be found in books covering the fundamental concepts of NMR spectroscopy (58,59). 

The problem we must address is how to recover the resonance frequencies present in a free-induction decay. We know that the FID curve is a sum of oscillating functions, so the problem is to analyze it into its component frequencies by carrying out a Fourier transformation. When the signal in Fig. 13.24a is transformed in this way, we get the frequency-domain spectrum shown in Fig. 13.24b. One Hne represents the Larmor frequency of the A nuclei and the other that of the X nuclei. 

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