Showing papers on "Spectral density published in 1989"

Nonlinear joint power spectrum based optical correlation.

Abstract: A nonlinear joint transform image correlator is investigated. The Fourier transform interference intensity is thresholded to provide higher correlation peak intensity and a better defined correlation spot. Analytical expressions for the thresholded joint power spectrum are provided. The effects of nonlinearity at the Fourier plane on the correlation signals at the output plane are investigated. The correlation signals are determined in terms of nonlinear characteristics of the spatial light modulator (SLM) at the Fourier plane. We show that thresholding the interference intensity results in a sum of infinite harmonic terms. Each harmonic term is envelope modulated due to the nonlinear characteristics of the device and phase modulated by m times the phase modulation of the nonthresholded joint power spectrum. The correct phase information about the correlation signal is recovered from the first-order harmonic of the thresholded interference intensity. We show that various types of autocorrelation signal can be produced simply by varying the severity of the nonlinearity and without the need to synthesize the specific matched filter. For example, the autocorrelation signal produced by a phase-only matched filter can be obtained by selecting the appropriate nonlinearity.

Turbulence in helium-gas free convection.

Abstract: Results on a Rayleigh-B\'enard experiment in helium gas at 5 K in a cylindrical cell of aspect ratio 1 are presented. The Rayleigh number spans a range from ${10}^{5}$ to ${10}^{12}$. A large-scale coherent flow is observed via the correlation of two adjacent temperature probes. This flow-velocity measurement shows clear transitions between different turbulent states. In hard turbulence, the dimensionless velocity [V/(\ensuremath{\kappa}/L)] scales with the Rayleigh number, with an exponent close to 1/2. The horizontal temperature difference across the cell is another measure of the different turbulent states. The temperature signals in the side-wall region (the large mean vertical velocity region) give clear pictures of various turbulent states. The measured velocity has been compared with the calculated free-fall velocity and also the heat transfer rate with the one calculated from the flow advection. The coherent frequency ${\ensuremath{\omega}}_{p}$ is found to be associated with the large-scale flow. In the side-wall region the power spectrum of the local temperature signal has a power-law dependence for Rayleigh numbers between ${10}^{8}$ and ${10}^{11}$. Both the exponent and the range of the power law change with the Rayleigh number. For Rayleigh numbers above ${10}^{11}$, a power law independent of Rayleigh number (exponent 1.4) develops at low frequency.

Analysis of Auditory Evoked Potentials by Magnitude-Squared Coherence

Abstract: Evoked potentials are usually analyzed in the time domain (voltage versus time). The most familiar frequency-domain measure, the power spectral density function, displays power as a function of frequency but doesn't distinguish signal power from noise power. The coherence function estimates,

A robust orthogonal algorithm for system identification and time-series analysis

Abstract: We describe and illustrate methods for obtaining a parsimonious sinusoidal series representation or model of biological time-series data. The methods are also used to identify nonlinear systems with unknown structure. A key aspect is a rapid search for significant terms to include in the model for the system or the time-series. For example, the methods use fast and robust orthogonal searches for significant frequencies in the time-series, and differ from conventional Fourier series analysis in several important respects. In particular, the frequencies in our resulting sinusoidal series need not be commensurate, nor integral multiples of the fundamental frequency corresponding to the record length. Freed of these restrictions, the methods produce a more economical sinusoidal series representation (than a Fourier series), finding the most significant frequencies first, and automatically determine model order. The methods are also capable of higher resolution than a conventional Fourier series analysis. In addition, the methods can cope with unequally-spaced or missing data, and are applicable to time-series corrupted by noise. Fially, we compare one of our methods with a wellknown technique for resolving sinusoidal signals in noise using published data for the test time-series.

Gravitational-wave measurements of the mass and angular momentum of a black hole.

Abstract: A deformed black hole produced in a cataclysmic astrophysical event should undergo damped vibrations which emit gravitational radiation. By fitting the observed gravitational waveform h(t) to the waveform predicted for black-hole vibrations, it should be possible to deduce the hole’s mass M and dimensionless rotation parameter a=(c/G)(angular momentum)/M^2. This paper estimates the accuracy with which M and a can be determined by optimal signal processing of data from laser-interferometer gravitational-wave detectors. It is assumed that the detector noise has a white spectrum and has been made Gaussian by cross correlation of detectors at different sites. Assuming, also, that only the most slowly damped mode (which has spheroidal harmonic indices l=m=2) is significantly excited—as probably will be the case for a hole formed by the coalescence of a neutron-star binary or a black-hole binary—it is found that the one-sigma uncertainties in M and a are ΔM/M≃2.2ρ^-1(1-a)^0.45, Δa≃5.9ρ^-1(1-a)^1.06, where ρ≃hs(πSh)^-1/2 (1-a)^-0.22. Here ρ is the amplitude signal-to-noise ratio at the output of the optimal filter, hs is the wave’s amplitude at the beginning of the vibrations, f is the wave’s frequency (the angular frequency ω divided by 2π), and Sh is the frequency-independent spectral density of the detectors’ noise. These formulas for ΔM and Δa are valid only for ρ≳10. Corrections to these approximate formulas are given in Table II.

Lattice-dynamical calculation of the Kapitza resistance between fcc lattices

Abstract: The temperature dependence of the Kapitza resistance (thermal boundary resistance) at the interface between two dissimilar solids is calculated for a model system consisting of two semi-infinite, harmonic fcc lattices in register. The spectral density of phonon flux transmitted across the interface is obtained from a numerical calculation of the phonon transmission coefficient and group velocity and is used to calculate the Kapitza resistance. Results for the spectral density of the transmitted phonon flux, the spectral dependence of the phonon transmission coefficient, and the temperature dependence of the thermal boundary resistance are presented. Calculation of the thermal boundary resistance for real systems using the results of this calculation is discussed.

Quantization noise in single-loop sigma-delta modulation with sinusoidal inputs

Abstract: An exact nonlinear difference equation is derived and solved for a simple sigma-delta modulator consisting of a discrete-time integrator and a binary quantizer inside a single feedback loop and an arbitrary input signal. It is shown that the system can be represented as an affine operation (discrete-time integration of a biased input) followed by a memoryless nonlinearity. An extension of the transform method for the analysis of nonlinear systems is applied to obtain formulas for first- and second-order time-average moments of the binary quantization noise, including the sample mean, energy, and autocorrelation. The results are applied to the special case of a sinusoidal input signal to evaluate these time averages and the power spectrum. In the limit of large oversampling ratios, the marginal moments behave as if the quantization noise had a uniform distribution. The spectrum is neither white nor continuous, however, even in the limit of large oversampling ratios. >

On the theory of carrier number fluctuations in MOS devices

Abstract: An analysis of the concept of input gate voltage spectral density in MOS devices is presented. It is shown that, within a carrier fluctuation model, the input gate voltage spectral density can be regarded as a flat band voltage spectral density S Vfb . It is demonstrated that the relationship between the drain current and flat band voltage spectral densities, S Id = g m 2 S Vfb , is applicable from the linear to the saturation regime of MOSFET operation.

Channel modeling and adaptive equalization of indoor radio channels

Abstract: The authors analyze the benefits of using a decision feedback equalizer (DFE) in the indoor radio environment and examine the results of performance predictions for different channel modelings. It is found that a QPSK/DFE modem with second-order diversity can operate at a data rate that is an order of magnitude higher than a QPSK (quadratic-phase-shift-keying) modem without equalization. A given set of measured profiles of the channel impulse response is interpreted using continuous and discrete channel models. The continuous channel model is represented by the delay power spectrum and the discrete channel model by the envelope delay power spectrum and the arrival rate of the paths. The sensitivity of the performance to the shape of the delay power spectrum, and the arrival rate of the paths is analyzed. >

Higher-order spectrum factorization in one and two dimensions with applications in signal modeling and nonminimum phase system identification

Abstract: The problem of modeling a given higher-order spectrum as that of the output of a linear time-invariant (LTI) system driven by a higher-order white random signal is discussed. This can be posed as a higher-order spectrum factorization problem. A theorem is provided to discuss the existence of such a factorization. A fast algorithm for efficient implementation of the higher-order spectrum factorization, if it exists, is then proposed. The results are extended to two dimensions straightforwardly. The relationship of the higher-order spectrum factorization problem to the well-known power spectrum factorization is also discussed. As applications, the problems of identification of nonminimum-phase LTI systems given the higher-order statistics of both input and output processes and phase reconstruction are presented. Experimental results are provided for the one-dimensional case. >

General phase modulation method for stored waveform inverse fourier transform excitation for fourier transform ion cyclotron resonance mass spectrometry

Abstract: A method for reducing the dynamic range of FT-ICR signal generated by the SWIFT technique includes the step of time shifting wave packets corresponding to segments of the Fourier spectral magnitude function to prevent coherent summing of the various frequency components of the excitation signal.

A Tutorial on Non-Parametric Bilinear Time-Frequency Signal Representations

Abstract: Nonstationary signals have a time-dependent spectral content. This is in contrast to stationary signals whose energy spectrum characterizes their spectral content and that is independent of time. Therefore, nonstationary signals require joint time—frequency representations.

Remarks on stochastic resonance.

Abstract: A recent and interesting experimental paper [B. McNamara, K. Wiesenfeld, and R. Roy, Phys. Rev. Lett. 60, 2626 (1988)] has refocused attention on the problem of stochastic resonance by presenting measurements of the singal-to-noise ratio (SNR) of a noise driven, periodically modulated bistable ring laser. We point out that the theoretical SNR, as defined in this and a previous work, is always infinity, because additive modulation leads to a \ensuremath{\delta} function in the power spectrum of the output. Quantitative information on stochastic resonance is contained in the strength of this \ensuremath{\delta} function relative to the noise background. We qualitatively reproduce the SNR data with an analog simulator using a standard quartic bistable potential. In this, as in previous experiments and simulations, a peak in the observed power spectrum is a reflection of the \ensuremath{\delta} function, but the amplitude of the peak is rendered finite (and hence measureable) only because of the finite resolution of the measurement system.

Quadratic Estimators of the Power Spectrum

Abstract: : Among nonparametric estimators of the power spectrum, quadratic estimators are the only ones that are dimensionally correct. This report motivates interest in quadratic estimators by setting up idealized experiments for spectrum analysis and deriving maximum likelihood estimates for narrowband power. These idealized experiments show that quadratic functions of the experimental data are sufficient statistics for estimating power. The maximum likelihood estimates show that low-rank projection operators play a fundamental role in the theory of spectrum analysis. The projection operator plays the same role as a bandpass filter in a conventional swept frequency spectrum analyzer. The mean-squared error of a maximum likelihood estimator of power is inversely proportional to the rank of the estimator. With our maximum likelihood result in hand, we turn to a systematic study of quadratic estimators of the power spectrum. Keywords: Heuristic methods, Covariance.

A real-time autoregressive spectrum analyzer for Doppler ultrasound signals

Abstract: A system based on a digital signal processor and a microcomputer has been programmed to estimate the maximum entropy autoregressive (AR) power spectrum of ultrasonic Doppler shift signals and display the results in the form of a sonogram in real-time on a computer screen. The system, which is based on a TMS 320C25 digital signal processor chip, calculates spectra with 128 frequency components from 64 samples of the Doppler signal. The samples are collected at a programmable rate of up to 40.96 kHz, and the computation of each spectrum takes typically 3.2 ms. The feasibility of on-line AR spectral estimation makes this type of analysis an attractive alternative to the more conventional fast Fourier transform approach to the analysis of Doppler ultrasound signals.

Noise power spectral characteristics of an inductively coupled plasma mass spectrometer

Abstract: The noise power spectra of {sup 85}Rb{sup +} signal and {sup 93}Nb{sup +} signal from an inductively coupled plasma mass spectrometer were measured at the same plasma conditions as were those of Sr II emission from the plasma itself. Comparison of these spectra showed that discrete frequency noise in the emission at the mass spectrometer sampling orifice is nearly identical with that in the mass spectrometric signal and that white noise in the mass spectrometer signal was higher than that found in the emission signal. The dependence of noise frequencies on plasma operating conditions was generally the same for both measurements and was generally the same as that expected of emission from the plasma alone, i.e., when the plasma was not being sampled for mass spectrometry. However, discrete frequency noise in emission from the plasma alone differed substantially in frequency from that in the mass spectrometric signal. These results indicate that the plasma is the source of discrete frequency noise in the mass spectrometric signal and that the discrete noise frequencies can be affected by changes in plasma gas dynamics due to interaction between the plasma and the mass spectrometer sampling interface. The major source of signal instability in thismore » particular inductively coupled plasma mass spectrometer was found to be 1/f noise.« less

Dissipation in macroscopic magnetization tunneling

Abstract: The effect of magnetoelastic dissipation upon the tunneling and coherence of the total magnetization in small (\ensuremath{\sim}100 A\r{}) single-domain ferromagnetic particles is investigated Such tunneling would be an example of a macroscopic quantum phenomenon It is shown that the dissipation has a super-Ohmic spectral density, J(\ensuremath{\omega})\ensuremath{\sim}${\ensuremath{\omega}}^{3}$, and that the dissipation is weak for reasonable material parameters Corrections to the rates, and the damping rate for coherent oscillations are obtained A key feature is the inclusion of the elastic waves in the medium surrounding the particle

A nonstationary signal simulation model for continuous wave and pulsed Doppler ultrasound

Abstract: A computer simulation model of the nonstationary Doppler ultrasound signals arising from pulsatile blood flow is presented. The model uses sinusoidal components that are modulated by a power spectral density function that varies over the cardiac cycle. An empirical model consisting of two exponential functions is used to represent both the continuous wave and pulsed Doppler power spectral density for normal carotid arteries. It is shown that the spectrogram speckle patterns of the synthesized Doppler signals compare very well with those clinically recorded. >

Application of bicoherence analysis in study of wave interactions in space plasma

Abstract: A spectral analysis at the second order (power spectrum) loses the phase information among the different Fourier components. To retain this information, the bispectrum (third order) and/or the bicoherence (normalized bispectrum) are calculated. Application to simulated data, shows the dependence of the bispectrum to amplitudes of involved waves and of the bicoherence to signal-to-noise ratio. Bicoherence technique is applied in the analysis of harmonics produced by an electronic receiver, as well as in the investigation of phase coherence between a ground-transmitter signal, a natural ELF emission near the proton gyrofrequency, and the sidebands around the carrier. Strong arguments are provided that the sidebands are generated by a parametric interaction between the transmitter signal and the ELF emission.

Making inflation work: Damping of density perturbations due to Planck energy cutoff.

Abstract: In this paper we propose an alternative method for the computation of classical density perturbations from a quantum field in an inflationary scenario. We compute the power spectrum of density perturbations directly from vacuum fluctuations of the ''time-time'' component of the energy-momentum tensor. We compute the inhomogeneous part of the correlation function for a massless minimally coupled scalar field in de Sitter space. The Fourier transform of this two-point function leads to the scale-invariant spectrum of perturbations, but is ultraviolet divergent. This expression can be made finite by introducing an (ad hoc) small-distance cutoff in the proper length. We argue that this cutoff should be of the order of the Planck length, and show that, in such a case, the density fluctuations have the acceptable magnitude (/similar to/10/sup -4/) for the case of primordial inflation. Thus the inflationary scenario can be made to work without any fine-tuning.

Effect of finite sampling on atmospheric spectra

Abstract: The effect of a finite averaging time on variances is well known, but its effect on power spectra is less clearly understood. We present numerical solutions for the spectral distortion arising from sampling over a finite time interval T and show that the commonly used filter function (1-sinc2πfT), valid for variances, is a reasonable approximation for power spectra only when T≥ 10τm, where / is the cyclic frequency, and τm is the dominant time scale of the process. Our results exhibit an increasingly steeper low-frequency roll-off as T decreases relative to τm, indicating that the measured spectrum is subject to a greater suppression of the lower frequencies (f < 1/T) than predicted by (1-sinc2πfT). This suppression is, in a sense, compensated by an overestimation of spectral estimates in the frequency range f ≥ 1/T.

Correction of non-linearities in detectors in fourier transform spectroscopy

Abstract: An interferogram is formed as in the prior art by dividing a beam of radiation from the source into two beams and interfering these beams so as to form an interferogram on the detector. A Fourier transform is then made of this interferogram. This transform has a signal spectrum above the cutoff frequency of the detector; and because of non-linearities in the detector and in the electronic signal processing circuitry, this transform also has a spectrum below the cutoff frequency of the detector. In accordance with the invention, two correction factors are calculated from this Fourier transform and these correction factors are then used to calculate a corrected interferogram. The first correction factor is evaluated by determining from the portion of the spectrum below the cutoff frequency a valve for the spectral signal at zero frequency. In addition, the integral of the square of the spectrum signal above the cutoff frequency is determined and the correction factor is found by dividing the signal at zero frequency by the integral of the square of the spectrum above the cutoff. The second correction factor is a function of the first correction factor and the integral of the spectrum signal above cutoff. These two corrections factors are then used in calculating a second order approximation to a corrected interferogram. Finally to produce the corrected Fourier transform, a Fourier transformation is made.

Multifunction Nonlinear Signal Processor: Deconvolution And Correlation

Abstract: We describe a multifunction nonlinear optical processor that can perform various types of operations such as image deconvolution and nonlinear correlation. This processor is joint power spectrum based and does not use any filters. In this technique both the input signal and the processing function are displayed side by side at the input plane of the processor. The joint power spectrum of the input signals is thresholded with varying nonlinearity to produce the specific operation. In image deconvolution the joint power spectrum is modified and hard clip thresholded to remove the amplitude distortion effects and to restore the correct phase of the original image. An amplitude mask averaged over an ensemble of images is assigned to the thresholded power spectrum to provide the amplitude magnitude of the restored image. In optical correlation, the Fourier transform interference intensity is thresholded to provide higher correlation peak intensity and a better defined correlation spot. We show that various types of correlation signals can be produced simply by varying the severity of the nonlinearity and without the need to synthesize the specific matched filter. For example, a phase-only correlation signal is produced by selecting the appropriate nonlinearity. An analysis of the nonlinear processor for image deconvolution is presented. Computer simulation of the proposed technique for a linearly smeared image is provided.

Electronic damping of adsorbate fundamental and overtone vibrations at metal surfaces

Abstract: A model calculation of the vibrational line shape of adsorbates at metal surfaces damped by the generation of electron-hole pairs is presented. Two vibrational excitations are considered, one fundamental and one overtone. To calculate the total absorption of a radiation field by the system, we use the formalism developed in the preceding paper to include contributions, ${\ensuremath{\alpha}}_{\ensuremath{\perp}}$ and ${\ensuremath{\alpha}}_{?}$, from the respective E-field components perpendicular and parallel to the surface. The generalized asymmetric Fano line-shape formula is shown to apply to both the fundamental and the overtone. For each case, the isotope effect on the line-shape parameters is obtained both in the limits of weak and strong breakdown of adiabaticity, where the weak- or strong-breakdown limit is modeled by assuming a flat spectral density near the Fermi level, or a sharp structure in that region on top of the flat part. It is found that a strong breakdown of adiabaticity weakens the isotope dependence of the asymmetry factor and the linewidth, while the isotope effect for the excitation strength remains the same as in the weak-breakdown limit. The magnitude of the excitation strength is modified as the strong-breakdown limit is reached. These conclusions remain valid whether the vibration contributes to ${\ensuremath{\alpha}}_{\ensuremath{\perp}}$ or to ${\ensuremath{\alpha}}_{?}$. When applied to the wag overtone of hydrogen on W(100), reasonably good agreement is found between the theory in the strong-breakdown limit and experiment assuming that the overtone absorption is given by ${\ensuremath{\alpha}}_{\ensuremath{\perp}}$, the perpendicular response. We also discuss other possibilities for the measured absorption, including the contribution from the overtone by ${\ensuremath{\alpha}}_{?}$, the tangential response, and from other excitations nearby in frequency.

Vibration control system

Abstract: A vibration control system for generating desired random vibration environment with a given reference Power Spectral Density (PSD) using a vibration generator on which a test object is fixed is disclosed A detected signal representing vibration of a test object is converted into a response spectrum by Fast Fourier Transform (FFT) and the response spectrum is compared with the reference spectrum to determine a drive spectrum Random drive signal having the determined drive spectrum amplitude is then generated continuously, and the signal is applied to a vibration generator on which the test object is fixed This signal must be random ie nonperiodic, and therefore consisting of continuous spectral components with sufficient statistical independence Method and facility to generate above mentioned signal are the principal of the present invention

A direct algorithm for computing 2-D AR power spectrum estimates

Abstract: An algorithm for computing the parameters in a 2-D autoregressive spectral estimate without prior estimation of the correlation is described. The algorithm utilizes the multichannel form of the Burg algorithm and the relation between multichannel and 2-D AR modeling. The procedure permits computation of the spectral matrix for several channels of 2-D data; models with support in different quadrants are combined to form the spectral estimate. >