Spectral amplitudes

The back wall echoes were sampled at 100 MHz and the length of these were 70 samples, yielding a size of the input data vectors, ) = 35. An example of such an echo is shown in Figure 2 together with its log spectral amplitude. 

In Figure 3 we see how the logarithm of the spectral amplitude effects the estimation results. For each component in input data vector, u, we have defined the feature relevance, Fn d), as... 

These coefficients (Equation 7.30) are required to calculate the transition probability or spectral amplitude (cf. Chapter 8). Note that for systems with more than two spin wavefunctions (S > 1/2) the energy eigenvalue problem is usually not solvable analytically (unless the matrix can be reduced to one of lower dimensionality because it has sufficient off-diagonal elements equal to zero) and numerical diagonalization is the only option. 

Figure 75-2 shows third-order data or a hyperspectral data cube where the spectral amplitude is measured at multiple frequencies (spectrum) with X and Y spatial dimensions included. Each plane in the figure represents the amplitude of the spectral signal at a single frequency for an X and Y coordinate spatial image. 

Figure 21.9 Pressure oscillation spectral amplitude as a function of injection timing. The two straight lines show the amplitude levels for uncontrolled cases...

To determine the dominant frequency of excitation, the near-fleld acoustic spectrum was obtained using a microphone. Typical near-fleld acoustic spectra for an excited jet and a natural jet are shown and compared in Fig. 29.5. When multiple peaks were observed in the spectrum, the peak with the highest spectral amplitude was denoted as the excitation frequency. By systematically varying the dimensions of the cavity, flow excitation occurred over a wide range of frequencies (4-40 kHz). Table 29.2 summarizes the normalized data. Initial tests were performed with semi-annular cavities to eliminate possible... 

Figure 6.3 Shaped femtosecond laser pulses from sinusoidal spectral phase modulation of an 800 nm, 20 fs FWHM input pulse. The left column shows the modulated pulses in the frequency domain, decomposed into spectral amplitude (gray line and background) and modulation...

Fig. 1. Demonstration of the phase control of femtosecond chirped pulses. Solid lines spectral phase of the diffracted pulse for two delays X and -X between the writing pulses. Thin dotted lines spectral phase difference between the 2 writing pulses for the two cases x and -X. The thin dashed line represents the spectral amplitude of the diffracted pulse. Insert spectral interference fringes between the unchirped and chirped writing pulses at time delay equal 0 at 800nm. The chirp is formed by propagation through a SF58 glass plate of thickness 1.7 cm.

Ephraim and Malah, 1983] Ephraim, Y. and Malah, D. (1983). Speech enhancement using optimal non-linear spectral amplitude estimation. In Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, pages 1118-1121, Boston. 

The essential difference between the field dependencies of the spectral amplitudes A2m and 2) , namely, the experimentally measurable Fourier components of Av and (Av)2, manifests itself atm >2. Below we take m = 2 and m = 3 as an example. As Figure 4.38 shows, the coefficients A4 and A in the range c0 < 20 increase monotonically, while the behavior of the amplitudes 4 and 6 is more complicated. In particular, each 2 curve at onH > 0 undergoes a minimum ( 2m =0) at a certain finite value These points constitute the following numerical sequence... 

The ESR spectral parameters of post-ischemic reperfused samples are similar to those of the control (Table 1). However, the spectral amplitude is consistently increased by a factor of two or more. Therefore, reperfusion of the ischemic myocardium results in an increase in the production of radicals. However, direct ESR evidence for the production of oxy radicals in ischemic and reperfused heart tissues is still lacking. 

Fig. 21. Changes in distance between R1 residues in TM3 and TM6. (A) Ribbon model of rhodopsin in the dark state showing the location of R1 side chains. For each distance measurement, only two R1 side chains were in the protein, one fixed at the reference site 139 in TM3, and the other at a site in the sequence 248-252. (B) After photoactivation, showing the movement of TM6 and the new positions of the pairs. (C) The corresponding EPR spectra of the double mutants in the dark (solid traces) and after photoactivation (light traces). A decrease in spectral amplitude represents a decrease in interspin distance.

M. Ohtsu, and T. Watanabe, Stack imaging of spectral amplitudes based on impact-echo for flaw detectionNDT E Int., 35, 189-196 (2002). 

To this end, the spin labeling technique was used to probe the active site structure of LADH in various solvent systems. The spin label, SL-1, alkylated cysteine 46 (12), an amino acid in the active site of LADH that normally serves as a ligand to the catalytic zinc ion. LADH is a dimer, and each monomeric subunit contains one firmly-bound catalytic zinc ion. The position of enzyme-bound SL-1 was estimated by the spin label-spin probe technique (14.15). Cobalt (II) was employed as the spin probe, and the catalytic zinc in the enzyme s active site was replaced by Co + according to the procedure of Sytkowski and Vallee (16). The EPR spectrum of enzyme-bound SL-1 was then measured before and after replacement of the active-site zinc by cobalt from the decrease in spectral amplitude the average nitroxide-metal distance was determined to be 4.8 1.5 A (17). 

The resulting value (A(fjj, x)) is related to that part of the frequency band which predominantly contributes to the spectral sum, i.e. to the arithmetic mean frequency (f j) of the spectral amplitude distribution within the i band. Subsequently, for a continuously moving window a series of attenuation coefficients (ot(f j)) is computed from the natural logarithm of the spectral ratio of the attenuated and reference signal... 

Fig. 2.14 Attenuation analysis by the smoothed spectral ratio method, (a) Definition of a moving window of bandwidth in which the spectral amplitudes are summed, (b) Seven attenuation curves analyzed from the...

In the next iteration, one can repeat the steps of (1) finding the most intense spectral amplitude and (2) subtraction of shifted PSF. The whole procedure should be continued until there are no significant peaks in the spectrum. This condition can be formulated as follows ... 

Since the linewidth of the spectra is a steep function of the interspin distance, empirical or semiempirical parameters such as spectral amplitude ratios or spectral second moment values were used to extract distances semiquantitatively and to answer structural questions in the past. In the following, the software available to extract distances and the caveats hidden in the analysis are presented. 

Experimentally, these line shapes appear in steady-state plots of dielectric or ultrasonic susceptibility versus frequency. The in-phase and 90 -out-of-phase dielectric spectral amplitudes can be combined in a method based on Hilbert transforms (see Chapter 4). 

Fig. 23. Temperature dependence of the spectral amplitude of nylon 6 for signal (II) in Fig 22...

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