Signal, free induction decay

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... 

Proton NMR measurements were made at 56.4 MHz on a spectrometer that was described previously (J5). Ti was measured with a 180°—f 90° pulse sequence, and lineshapes were determined from free-induction decay signals following a 1-2 fLsec 90° pulse. T p was measured with a 90° x-pulse followed by an attenuated t/-pulse whose length was varied from 10 usec to 40 msec. 

Figure 10.4 Free induction decay signal, which appears in the receiver coils after a 90° pulse. The FID is a time-domain spectrum, showing RF intensity as a function of time 12- It is a composite of the RF absorption frequencies of all nuclei in the sample. The Fourier transform decomposes an FID into its component frequencies, giving a spectrum like that shown in Fig. 10.1. Figure generously provided by Professor John M. Louis.

How do we extract the chemical shifts of all nuclei in the sample from the free-induction decay signal The answer is our old friend the Fourier transform. The FID is called a time-domain signal because it is a plot of the oscillating and decaying RF intensity versus time, as shown in Fig. 10.4 (the time axis is conventionally labeled t2, for reasons you will see shortly). Fourier transforming the FID produces afrequency-domain spectrum, a plot of RF intensity versus the frequencies present in the FID signal, with the frequency axis labeled v2 for frequency or F2 for chemical shift, as shown in Fig. 10.1. So the Fourier transform decomposes the FID into its component frequencies, revealing the chemical shifts of the nuclei in the sample. 

Digital Processing of the Free-induction, Decay Signal. 50... 

Fig. 3.—Fourier-transform, Proton Magnetic Resonance Spectra45 of 6-Deoxy-l,2 3,4-di-O-isopropylidene-6-phthalimido-a-D-gaIactopyranose (54) (0.06 mg) at 90 MHz, Obtained by Transformation (N = 4,096) of the Free-induction Decay Signal (1,024 Datum Points, see Fig. 2), After the Appendation of 3,072 Zero, Datum Points ( Zerofilling, See Text), [(a) Spectrum associated with the real part of the transform, and (b) with the imaginary part (c) absorption-mode spectrum computed by phase correction of the spectrum in (a) and (d) dispersion-mode spectrum computed by phase correction of the spectrum in (b). Parameters for phase correction, A —255° and B —215°. Note that the phase of the tetramethylsilane and chloroform signals in (c) is slightly different from that of the carbohydrate derivative. By coincidence, the peak for residual water in spectrum (c) has almost the same intensity as the methyl signals, and could have been mistaken for one, had other spectra not been recorded.]...

Fig. 4.—(a) Proton, Free-induction Decay Signal (1,024 datum points) of 6-Deoxy-l,2 3,4-di-0-isopropylidene-6-phthalimido-a-D-gaIactopyranose (54) (0.06 mg), Obtained48 in the Same Way as the Signal Shown in Fig. 2, Except that 16,384 Pulses at 90 MHz Were Used, Together with Signal-averaging Over a Period of 112 min.

Modern instruments are Fourier transform NMR, which use a constant magnetic field commonly produced by a superconducting magnet and a strong radio-frequency pulse that irradiates the sample. The free induction decay signal emission of the sample is... 

Imaging is not the only way of measuring fruit quality. Relaxation time measurements can also be useful the free induction decay signal from prunes can be analysed as containing two components that correspond to water and soluble solids. The intensity of the soluble solids signal corresponds well to those... 

The maximum amplitude of the free induction decay signal Mfid/ generated by a single pulse, is achieved immediately after the end of the pulse and can be determined from Equation (22)... 

It follows from Equation (43) that the maximum amplitude of fhe signal creafed by sequence MW-4 equals the maximum amplitude of the free induction decay signal Mfid and is achieved at... 

A microwave pulse from a tunable oscillator is injected into the cavity by an antenna, and creates a coherent superposition of rotational states. In the absence of collisions, this superposition emits a free-induction decay signal, which is detected with an antenna-coupled microwave mixer similar to those used in molecular astrophysics. The data are collected in the time domain and Fourier transformed to yield the spectrum whose bandwidth is determined by the quality factor of the cavity. Hence, such instruments are called Fourier transform microwave (FTMW) spectrometers (or Flygare-Balle spectrometers, after the inventors). FTMW instruments are extraordinarily sensitive, and can be used to examine a wide range of stable molecules as well as highly transient or reactive species such as hydrogen-bonded or refractory clusters [29, 30]. 

In Fig. 27 we reproduce a low-temperature optical free induction decay signal of pentacene-A,4 in p-terphenyl. The insert in the figure shows that... 

Fig. 27. Optical free induction decay signal of pentacene-/ii4 in p-terphenyl at 1.5...

In another series of diffusion experiments, as-postcured epoxies were first immersed in 23°C heavy water for 2 months. Then the temperature of the epoxy/heavy water interacting system was increased to 40 C. The continuous influx of heavy water into the epoxy can be easily monitored by deuterium NMR spectroscopy. The free induction-decay signal as normalized by the specimen weight showed an increase as a function of sorption time (see Figure 23). For example, a 2 month room-temperature sorption results in an epoxy having 2.10% of moisture (determined by gravimetry). With... 

After the excitation pulse is turned off, the spin system emits the energy, returning to thermal equilibrium of the spin states. The signal observed in this process is called the FID (Free Induction Decay) signal, which is a spectrum recorded in the time domain. 

P15.17 The shape of spectral line T(w) is related to the free induction decay signal G(r) by IUo)=ciRef Gine dt... 

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