Ratio Of Power Spectrum Research Articles

The non-linear redshift-space power spectrum of galaxies

We study the power spectrum of galaxies in redshift space, with third-order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e., the galaxy density is sampled from some local function of the underlying mass distribution. We find that the effect of the non-linear bias in real space is to introduce two new features: first, there is a contribution to the power which is constant with wavenumber, whose nature we reveal as essentially a shot-noise term. In principle this contribution can mask the primordial power spectrum, and could limit the accuracy with which the latter might be measured on very large scales. Secondly, the effect of second- and third-order bias is to modify the effective bias (defined as the square root of the ratio of galaxy power spectrum to matter power spectrum). The effective bias is almost scale-independent over a wide range of scales. These general conclusions also hold in redshift space. In addition, we have investigated the distortion of the power spectrum by peculiar velocities, which may be used to constrain the density of the Universe. We look at the quadrupole-to-monopole ratio, and find that higher order terms can mimic linear theory bias, but the bias implied is neither the linear bias, nor the effective bias referred to above. We test the theory with biased N-body simulations, and find excellent agreement in both real and redshift space, providing the local biasing is applied on a scale whose fractional rms density fluctuations are < 0.5.

Operational Deflection Shape Analysis of Multiple Exciting Sources with Random Noise.

This paper investigates operational deflection shape analysis using multi-channel time history response. One of the problems in the case of multi-channel data acquisition is noise from the sensors. Operating vibration characteristics are obtained using principal component analysis or the response-ratio method. Principal component analysis is a technique to determine unknown force input and operational deflection shape. The response-ratio method is a technique to determine operational deflection shape from the ratio of power spectra. This paper describes noise reduction in operational deflection shape using principal component analysis and the response-ratio method. Noise reduction is verified by the correlation function on frequency domain. The ratio of noise reduction is improved more using principal component analysis rather than the response-ratio method. The correlation on frequency domain is able to accurately determine the operational deflection shape.

Computer evaluation of cat brain activation by means of striate cortex ecog

We analyzed striate cortex electrocorticograms of 12 cats in the following states: at rest with eyes closed and with eyes open; after light electrical stimulation of the ears; drowsiness; opening of the eyes after drowsiness; narcotic sleep. Spectral and periodometric analyses of the ECOG revealed state-dependent differences in power spectra from cats in two frequency bands (2.8–5.0 and 13.8–20.8 Hz). It is suggested that the ratio of ECOG power spectra in these frequency bands can be used to evaluate brain activation in cats.

The depth dependence of seismic background noise within the sea floor

Further results are reported of a study of seafloor noise using an array of ocean-bottom seismometers in a sediment pond in deep water off the California coast. Earlier (Schreiner and Dorman, 1990) measurements were presented of coherence between elements of the array that contained interelement spacings in the 8–156 m range and it was shown that they represented the fundamental and first three overtones of seismic surface and interface waves. Here, the ratios of power spectra (horizontal to vertical component) in the 0.500–10 Hz frequency band were used to refine the estimates of the interface wave mode excitation that were made earlier using the interelement coherences. There is a simple frequency dependence in the mode excitation functions. The fundamental mode dominated below 0.65 Hz and is succeeded by the first three overtones in order as the frequency increases. The other transition frequencies are 0.95 and 6.5 Hz. From these excitation functions, the depth dependence of background noise was synthesized, using the vertical wave functions from the known shear velocity structure. For some depths in the 0.8–10 Hz frequency range, the amplitude of vertical component noise is up to 29 dB greater than at the surface, due to the prominence of higher mode interface waves in this band. Varying degrees of noise suppression are obtained outside this band. The noise suppression (or enhancement) is strongly dependent on the relative mode excitation. At frequencies where the fundamental mode dominates there will be noise reduction downhole while at frequencies where the overtones are prominent, there will be noise enhancement at some depths. For horizontal-component noise there is noise suppression with depth at all frequencies. [Work supported by ONR and ONT.]

Multi-look versus single-look processing of synthetic aperture radar images with respect to ocean wave spectra estimation

Abstract Full-bandwidth C-band synthetic aperture radar (SAR) data are compared with 7-look and 3-look data. The peak-to-background ratio of the image intensity power spectrum describing the wave detectability is found to be on average 8-9dB higher for the 7-look data and 2-5dB higher for the 3-look data than the single-look data. This is mainly due to the decrease in the speckle noise level when going from single-look to multi-look processing. In addition, look-sum processing is evaluated against spectral-sum processing for various temporal look separations. A significant improvement in image spectral peak contrast is observed for the spectral-sum data versus the look-sum data, with increasing temporal separations between the looks. No such improvement is observed in the corresponding image spectral noise contrast parameter. These observations are in agreement with the spatial misregistration inherent in look-sum data. Finally, the acceleration contribution to the observed aximuth smearing in the spectra...

Quantization and truncation effects on binary joint transform correlation

Analysis of the quantization effects of the binarized joint power spectrum on the performance of the binary joint transform correlator (JTC) is investigated. The signal to noise ratio (SNR) of the binarized joint power spectrum is determined for various levels of the Fourier plane quantization of the binary JTC. The SNR is computed for the truncated binarized joint power spectrum plane and the binary JTC performance is determined for various levels of Fourier plane truncation. Analytical expression are derived for the capture effect of the binary JTC in the presence of the Fourier plane quantization. Nonlinear compression or truncation in the Fourier plane can improve the performance of the binary JTC at low quantization levels. Computer simulation is used to verify the results of the theoretical analysis.

EEG Spectral Changes during One-Dimensional Hand-Tracking

For our study of change in spectral power in the EEG (alpha and beta bands) when subjects were on and off target during one-dimensional hand-tracking, 11 healthy paid subjects, 8 men and 3 women of mean age 23.4 yr., volunteered to participate in the experiments. During 3-min. tracking task (1) the subject had to keep a joystick on a light-spot inside the given target (two vertical bars) which moved horizontally across the CRT screen. The instant a subject failed to keep the light-spot within target limits was scored as a tracking error (OUTevent). The return into the target was evaluated as error correction (IN event). EEG was recorded during the whole series of 8 tracking tasks, differing in target size (10 and 20 rnm), type of target movement (continuous and interrupted), and target speed (constant and feedback modified) (2) from O,, 0, and C,, C, (according to the 10120 system of electrode locations) by means of nonpolarizing AgtAgC1 electrodes. Linked earlobe electrodes served as the common reference. The power spectra in alpha and beta bands were chosen as main spectral characteristics of EEG as several subjects showed suppression of EEG alpha activity recorded on 0, and 0, positions after tracking error in pilot experiments. To describe the relationship between the tracking (IN/OUT) events and occurrence of EEG alpha and beta activity, the following method was adopted. Using a Fast Fourier Transformation (FFT) procedure, pairs of power spectra were calculated in averaged l-sec. EEG intervals with IN and OUT events located in their center. Then the ratios of power spectra for the alpha and beta frequency bands to the total power spectra were calculated. The frequency bands were set to 8-13 Hz for alpha and 13-24 Hz for beta activity. It followed from the comparisons of all values obtained (pooled together as the results were similar on all the tasks) that in 65% of cases the power of EEG alpha activity on 0, and 0, was lower immediately after OUT events than before them (by 5.8% p< .05), whereas in 62% the power of beta activity became lower on C, and C, immediately after IN events than before them (by 1.2%). It might be assumed that stereotyped manual cracking is often combined with a prevalence of alpha activity in EEG whereas on an out-ol-larger s~tuation voluntary effort toward error correction is accompanied by an increase of power in be~a band.

Examination of a dual wavelength doppler radar technique to measure vertical wind velocity and drop - size distributions

Estimates of drop-size distributions aloft derived from the Doppler velocity spectrum are sensitive to errors in the vertical wind estimate. A technique to deduce vertical velocity from the ratio of power spectra obtained from two vertically pointing radars operating at two different wavelengths is theoretically examined. Using an assumed distribution, ratios of spectral density were computed for clouds composed of water, ice, or water-coated ice, and are presented for a sample of radar wavelengths. These ratios are uniquely related to the vertical wind, and allow its determination independent of an assumed drop-size distribution. Historically, the interdependence between drop-size distribution and vertical wind has limited the accuracy from which either could be deduced. The effect of errors in estimating the temperature of the precipitation and fluctuations in the power spectral estimates are derived for simulated drop-size spectra. Data processing techniques are suggested and the sampling time necessary to estimate the vertical velocity to within 30 cm sec −1 is given.