Spectral power density

Goldfisher, Autocorrelation function and power spectral density of laser-produced speckle pattern . J. Opt. Soc. Am., vol.55, p.247(1965). 

Blackbody Emittance. Representative blackbody emittance (9,10), calculated as a power spectral density, is shown in Figure 2. The wavelength, X, of peak power density for a blackbody at temperature, T, is given by Wien s displacement law ... 

If the surface (i.e., the best fit plane) is in the x—y plane, and Z x,y) is the surface height variation (surface roughness) relative to that plane, the power spectral density is given by... 

Although the power spectral density contains information about the surface roughness, it is often convenient to describe the surface roughness in terms of a single number or quantity. The most commonly used surface-finish parameter is the root-mean-squared (rms) roughness a. The rms roughness is given in terms of the instrument s band width and modulation transfer function, M(p, q) as... 

The framework we adopted for measuring the scaling behavior from AFM images is the following. The 2-D power spectral density (PSD) of the Fast Fourier Transform of the topography h(x, y) is estimated [541, then averaged over the azimuthal angle

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Noise is characterized by the time dependence of noise amplitude A. The measured value of A (the instantaneous value of potential or current) depends to some extent on the time resolution of the measuring device (its frequency bandwidth A/). Since noise always is a signal of alternating sign, its intensity is characterized in terms of the mean square of amplitude, A, over the frequency range A/, and is called (somewhat unfortunately) noise power. The Fourier transform of the experimental time dependence of noise intensity leads to the frequency dependence of noise intensity. In the literature these curves became known as PSD (power spectral density) plots. 

Since diffusing species move randomly in all directions, the diffusing species may sense the self-affine fractal surface and the self-similar fractal surface in quite different ways. Nevertheless a little attention has been paid to diffusion towards self-affine fractal electrodes. Only a few researchers have realized this problem Borosy et al.148 reported that diffusion towards self-affine fractal surface leads to the conventional Cottrell relation rather than the generalized Cottrell relation, and Kant149,150 discussed the anomalous current transient behavior of the self-affine fractal surface in terms of power spectral density of the surface. 

The measured spin relaxation parameters (longitudinal and transverse relaxation rates, Ri and P2> and heteronuclear steady-state NOE) are directly related to power spectral densities (SD). These spectral densities, J(w), are related via Fourier transformation with the corresponding correlation functions of reorientional motion. In the case of the backbone amide 15N nucleus, where the major sources of relaxation are dipolar interaction with directly bonded H and 15N CSA, the standard equations read [21] ... 

Figure 24.4 Measurements of gas temperature recorded at 3-kilohertz rate at x/d = 2 in the 5-kilowatt combustor (a) and the power spectral density (1-hertz resolution) of a 1-second history of the temperature measurements (6). Steady parameters = 0.75, fo = 100 Hz, Aair = 25 W, and 6 tuei = 200°...

G(to) - power spectral density t 5= time constants c = constant... 

Fig. 6 Trace (a) is the power spectral density of the original spectrum o(x), trace (e) the power spectral density of the convolved spectrum /(jc). Traces (b), (c), and (d) are the power spectra of the following smoothing filters 5-point quadratic, 13-point quartic, and multismooth (a convolution of a 5-point quadratic, a 7-point quadratic, an 11-point quartic, and a 13-point quartic.

Figure 6.6 Two-state quantum system driven on resonance by an intense ultrashort (broadband) laser pulse. The power spectral density (PSD) is plotted on the left-hand side. The ground state 11) is assumed to have s-symmetry as indicated by the spherically symmetric spatial electron distribution on the right-hand side. The excited state 12) is ap-state allowing for electric dipole transitions. Both states are coupled by the dipole matrix element. The dipole coupling between the shaped laser field and the system is described by the Rabi frequency Qji (6 = f 2i mod(6Iti-...

Wi Power spectral density for black body radiator W/m3 ML ... 

Cancelling of the signal. For a sinusoidal signal of frequency 0 (which is supposed to correspond to the center frequency of one of the filters of the filter-bank), it is easily checked (assuming that the additional noise power spectral density is sufficiently smooth) that Eq. 4.18 becomes... 

This suppression rule is derived by analogy with the well-known Wiener filtering formula replacing die power spectral density of die noisy signal by its periodogram estimate. 

More precisely, die quantity displayed is the signal power estimated from 10ms frames. As die power spectral densities of die two types of noise exhibit a strong peak at the null frequency, the two noises were pre-whitened by use of an all-pole filter [Cappe, 1991]. This pre-processing guarantees that the noise autocorrelation functions decay sufficiently fast to obtain a robust power estimate even with short frame durations [Kay, 1993]. 

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