Average power spectrum

Figure 21. Typical average power spectrum plots of the bed density fluctuations measured along the bed height with the 40.6-cm jet assembly (Set Point 9).

FIGURE 9.26 Averaged power spectrum of detector signals for 500-pm... 

The ice force records are digitized based on the Nyquist frequency criterion. Fluid-structure interaction is considered in an approximate manner using the frequency-independent added mass concept, i.e. added mass equal to the mass of water displaced. The equivalent evolutionary white noise, is based on the maximum peak of the averaged power spectrum and the evolutionary white noise is considered as a two-segment piece-wise linear function, as shown in Fig 3. The random excitation, Y(t), can be decomposed as follows ... 

Results from Eq. (1) are averaged over all jy-coordinate of the image and an average power spectrum (APS) is obtained for each angular position ... 

Fuentes NO, Favret EA. (2002) A new surface characterization technique RIMAPS (Rotated Image with Maximun Average Power Spectrum)./Afitrotc 206 72—83. 

Favret EA, Fuentes NO, Molina AM, Setten L. (2008) Description and interpretation of the bracts epidermis of Gramineae (Poaceae) with rotated image with maximum average power spectrum (RIMAPS) technique. Micron 39 985-991. 

Finding the values of G allows the determination of the frequency-domain spectrum. The power-spectrum function, which may be closely approximated by a constant times the square of G f), is used to determine the amount of power in each frequency spectrum component. The function that results is a positive real quantity and has units of volts squared. From the power spectra, broadband noise may be attenuated so that primary spectral components may be identified. This attenuation is done by a digital process of ensemble averaging, which is a point-by-point average of a squared-spectra set. 

FIG. 14 Example of simulated oscillations in the rate of CO2 production (left) and its power spectrum averaged over 10 simulation runs. (From Ref. 15.)... 

Figure 4. Improvement in sensitivity with the CAT. PFA and a reference peak at m/e 315. The observed improvement in signal-to-noise ratio results from the longer total scanning time and also the fact that many sweeps are made during this time. The overall improvement in signal-to-noise ratio depends on the detailed power spectrum of the noise (9). Resolution 12,000 here and for all following time averaged spectra...

To measure the strength of the forces exerted on particles, various analytical techniques have been developed [6, 7]. Unfortunately, since most of these techniques are based on hydrodynamics, assumption of the potential profiles is required and the viscosities of the fiuid and the particle sizes must be precisely determined in separate experiments, for example, using the viscous flow technique [8,9] and power spectrum analysis of position fluctuation [10]. Furthermore, these methods provide information on ensemble averages for a mass of many particles. The sizes, shapes, and physical and chemical properties of individual particles may be different from each other, which will result in a variety of force strengths. Thus, single-particle... 

Figure 8.4. Transmission electron micrograph showing hexagonal close-packed Ag nanocrystals (diameter 7 nm) obtained by evaporating a chloroform dispersion on a carbon substrate. The average interparticle distance is 1.5 nm. The inset shows the two-dimensional power spectrum of the image (reproduced with permission from reference...

Fig. 3.11 (a) Averaged Raman spectrum of 50 different NIH/3T3 fibroblast cells measured at a 785 nm excitation wavelength, 50 mW laser power at the sample for 180 s. (b-e) SER spectra taken by excitation of NS in different cells at the same wavelength with 5 s acquisition time and 3 mW laser power at the sample [56]... 

For the 9,000 m deep KTB scientific hole, heat production measurements were made with an average sampling interval of 3 m. The power spectrum of the vertical (one-dimensional) heat production profile appears to follow a power law oc K with /3 = 1.73 (Figure 6). Using this value for the one dimensional spectral slope, we obtain the exponent of the three-dimensional power spectrum using the equation /33 = /3i -f 2. (e.g., Maus and Dimri, 1994). We then find that the power spectrum of the surface heat flow Pq(K) oc This is a very smooth function,... 

The averaging is over all particles and many indejjendent time origins. 3, Power spectrum,... 

For our purpose the important moments are ( x p), sometimes referred to as the average strengths of the Fourier components The power spectrum I (co) of the stochastic process is defined as the T -> oo limit of the average intensity at frequency m ... 

Equation (4.3.5) is the Fourier transform of the linear correlation (4.3.1). This relationship is referred to as the correlation theorem. If x(t) is white noise, then ensemble averages have to be incorporated into equations (4.3.5)-(4.3.7), because the power spectrum of white noise is again white noise, but with a variance as large as its mean value [Beni]. When the linear correlation theorem (4.3.5) is applied to the same functions, then Ci((o) is the power spectrum of Y((o) = X co). Conversely, Ci(w) is then the Fourier transform of the auto-correlation function of y(f) = x(t) (cf. eqn 4.3.1). 

Raman spectra obtained by subtracting the spectra from the two genotypes. The acquisition times were 7-15 min for each spectrum and the laser pulse energy was 340pJ (average power 340mW, 1 kHz repetition rate). Reproduced with permission from Ref [39] American Society for Bone and Mineral Research. 

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