Signal envelope

No solid state NMR experiment is able to obtain spectra comparable to those routinely recorded in the liquid state. Thus multiplets become broad singlets and, if close together, overlap to give a broad signal envelope . While the differentiation of aromatic and aliphatic protons is simple, the information available is, from the point of view of structure determination, very limited. Thus we shall not provide an example. 

Figure 3.19. Data in Figure 3.15, with the signal envelope shown by the dashed lines. The half-life of the signal is 11/2, about 0.33 time units. 

The two heavily faulted mordenites (Samples 2 and 3) gave a calculated Si/Al ratio different from that obtained from chemical analyses (Table III). Both samples displayed a single resonance at about 52 ppm in their corresponding aluminum-27 spectrum. Besides the expected silicon-29 resonances at -98.4, -105.8 and -114.2 ppm, Sample 2 displayed a broad signal envelope that extended almost up... 

For (fi =Ti Equation (117) coincides with the expression for the signal envelopes observed upon the action of sequence (108) with (f = n. 

Note that the mass flux is a vector quantity and Fn stands for the flux in the direction of velocity component un. Since this velocity component is connected with the individual realizations, the integral value according to Equation 7.34 is introduced in Equation 7.41 for convenience. The volume integral of the Doppler signal envelope in the denominator is obtained from the logarithmic mean amplitude (LMA) method (Qiu and Sommerfeld 1992). A detailed derivation for the determination of this integral is given by Sommerfeld and Qiu (1995). 

Here, s0 0, i) is the signal envelope in the indirect dimension, q is the number of angles that differ from 0° or 90° (the number of subspectra to be combined for quadrature detection is 2q[, 15]), andn(/) is the operator-chosen number of scans recorded for each of the subspectra. hm 0, i) is the applied window function, tmax( ) the maximal evolution time, and M 0) the number of indirect points sampled. 

FIGURE 31.9 Synchronization scheme of envelopes of stimulation signals at various channels. (Note Broken vertical lines divide between the four Parastep menus. Paraspinal signal envelopes correspond in shape to quadriceps channels... 

An example for the experimental data obtained approximately 2 mm behind the nozzle is presented in Fig. 6. The coherent anti-Stokes Raman signal S ° (tj,) is plotted versus delay time. The data points extend over 4 orders of magnitude and represent an average of 20 individual measurements. A complicated beating structure and the decay of the signal envelope are readily seen. 

Define the received power as w=r l, where r is the received signal envelope. Let p(W) be the probability density function of the power W, where W = 10 log w. In a lognormal environment r has a lognormal distribution and... 

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