Showing papers on "Spectral density published in 1986"

Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP)

Abstract: Minimum shift keying and offset QPSK are two well-known modulations which can be interpreted as a set of time/phase-shifted AM pulses. We show in this paper that any constant amplitude binary phase modulation can also be expressed as a sum of a finite number of time limited amplitude modulated pulses (AMP decomposition). New methods for computing autocorrelation and power frequency spectrum are derived, which give very simple results for half-integer index modulations. We also show that the signal can be built with good accuracy using only one optimized pulse ("main pulse"). This synthesis is particularly satisfactory for modulations that have good spectral characteristics and/ or low index.

Fractional Brownian Motion: A Maximum Likelihood Estimator and Its Application to Image Texture

Abstract: Fractals have been shown to be useful in characterizing texture in a variety of contexts. Use of this methodology normally involves measurement of a parameter H, which is directly related to fractal dimension. In this work the basic theory of fractional Brownian motion is extended to the discrete case. It is shown that the power spectral density of such a discrete process is only approximately proportional to |f|a instead of in direct proportion as in the continuous case. An asymptotic Cramer-Rao bound is derived for the variance of an estimate of H. Subsequently, a maximum likelihood estimator (MLE) is developed to estimate H. It is shown that the variance of this estimator nearly achieves the minimum bound. A generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the MLE when the discrete fractional Brownian process is contaminated with additive Gaussian noise. The results show that even at signal-to-noise ratios of 30 dB, significant errors in estimation of H can result when noise is present. The MLE is then applied to X-ray images of the human calcaneus to demonstrate how the line-to-line formulation can be applied to the two-dimensional case. These results indicate that it has strong potential for quantifying texture.

Linewidth determination from self-heterodyne measurements with subcoherence delay times

Abstract: The behavior of the power spectrum of an external cavity semiconductor laser has been studied using a delayed self-heterodyne interferometric technique that uses delay times less than the laser's coherence time. Experimental results show that the resulting power spectrum is consistent with the theoretical model. However, there is evidence that additional frequency fluctuations are present that cause the delta function portion of the power spectrum to have a finite width.

The Sponge-like Topology of Large-Scale Structure in the Universe

Abstract: We describe and apply a quantitative measure of the topology of large scale structure: the genus of density contours in a smoothed density distribution. For random phase (gaussian) density fields, the mean genus per unit volume exhibits a universal dependence on threshold density, with a normalizing factor that can be calculated from the power spectrum. The topology of the observational sample is consistent with the random phase, cold dark matter model.

Resonances of chaotic dynamical systems.

Abstract: We present analytic properties of the power spectrum for a class of chaotic dynamical systems (Axiom-A systems). The power spectrum is meromorphic in a strip; the position of the poles (resonances) depends on the system considered, but only their residues depend on the observable monitored. In relation with these results we also discuss the exponential or nonexponential decay of correlation functions at infinity. In conclusion, it appears desirable to analyze the decay of correlation functions and the possible analyticity of power spectra for physical time evolutions, and for computer generated simple dynamical systems (non-Axiom-A in general).

Power spectra of fluid velocities measured by laser Doppler velocimetry

Abstract: The power spectrum and the correlation of the laser Doppler velocimeter velocity signal obtained by sampling and holding the velocity at each new Doppler burst are studied Theory valid for low fluctuation intensity flows shows that the measured spectrum is filtered at the mean sample rate and that it contains a filtered white noise spectrum caused by the steps in the sample and hold signal In the limit of high data density, the step noise vanishes and the sample and hold signal is statistically unbiased for any turbulence intensity

Statistical properties of dynamic speckles

Abstract: The statistical properties of dynamic speckles produced by a moving diffuse object were reviewed by providing the space–time correlation function and the power spectrum of speckle-intensity fluctuation for five combined cases of both the optical configuration and the illumination light. In the optical configuration, three kinds of geometry (free-space, single-lens, and double-lens) were taken, and three kinds of illumination light (a Gaussian beam, a plane-wave beam, and a Gaussian Schell-model beam) were used. Consequently, it was shown that the cross-correlation function and the power spectrum are both Gaussian under some assumptions. From the dynamic properties, two types of speckle motion, boiling and translation, were also evaluated for various conditions of object motion, optical configuration, and illumination light.

Amplitude squeezing in a semiconductor laser using quantum nondemolition measurement and negative feedback.

Abstract: A new scheme for generating an amplitude-squeezed state is proposed The photon-flux fluctuation of a semiconductor-laser output wave is measured with a quantum nondemolition (QND) detector, and is negatively fed back to the laser pumping current The operator Langevin equations are derived by combining the quantum-mechanical analyses on the laser internal-external field fluctuations, the quantum nondemolition detector based on an optical Kerr effect, and a negative-feedback circuit The output wave features a reduced photon number noise below the standard quantum limit, 〈(\ensuremath{\Delta}n^${)}^{2}$〉^〉, and an enhanced phase noise above that, 〈(\ensuremath{\Delta}\ensuremath{\psi}^${)}^{2}$〉g(1/4)〈n^${〉}^{\mathrm{\ensuremath{-}}1}$, while the minimum uncertainty product is still preserved The observed photoelectron statistics in a negative-feedback GaAs laser diode using a conventional p-i-n photodiode (not a QND detector) are shown to exhibit sub-Poissonian statistics with the variance 〈(\ensuremath{\Delta}n^${)}^{2}$〉apeq2026〈n^〉 The measured photocurrent fluctuation spectral density is also indicated to be below the standard quantum limit by a factor of 02 (=-7 dB) The experimental results also confirm that such amplitude squeezing is only observed inside the feedback loop and cannot be extracted from the loop unless a quantum nondemolition detector is used

Adaptive noise suppressor

Abstract: An adaptive noise suppressor for providing noise filtered signals. The noise suppression device employs a vector gain μ for the weights of the filter wherein the vector μ is selected for each frequency bin to be inversely proportional to the power spectrum. A projection operator is utilized to remove the effects of circular convolution to produce a linear convolution result wherein the weights are readjusted in a manner to minimize the difference between the input signal and the filter output signal, thereby minimizing the error signal to produce a noise suppressed signal in the filtered output. A frequency suppression device utilizes the same principles of the vector μ and projection operator, but the output is taken from the error output of the filter.

Tailored excitation for trapped ion mass spectrometry

Abstract: An ion cyclotron resonance cell has applied thereto an excitation which has a time domain waveform which is the inverse Fourier transform of a frequency domain excitation spectrum which has been chosen by the user to yield selective excitation and/or suppression of ranges of ion mass-to-charge ratios. To minimize the dynamic range of the time domain signal resulting from the inverse Fourier transform, the phases of the various discrete frequency components in the frequency domain spectrum which are used in calculating the inverse Fourier transform are not constant but rather are varied as a function of the frequency of the components. The phase of each component is assigned such that the frequency components in the time domain signal are not all in phase at any point in time, thereby avoiding large magnitude spikes in the time domain waveform. The phases of the various frequency components may follow a non-linear function of the frequencies of the components, such as a quadratic function. By varying phase in this manner, the time domain signal which is applied to the excitation plates of the ion cyclotron resonance cell has a frequency domain power spectrum which is substantially flat over the specified band or bands of frequencies of interest. The time domain waveform may be shifted and/or weighted before being applied to the excitation plates. Tailored excitation may also be applied in this manner to the end plates of an ion trap cell to cause tailored ejection of specific bands or ranges of ions with retention of remaining ions within the cell.

Random vibration of structures

Abstract: Stationary Random Process, Autocorrellation and Spectral Density Ergodic Processes and Temporal Statistics Models of Random Excitations Structures with Single Degree of Freedom (SDOF) Response of Linear Multidegree-of-Freedom (MDOF) Systems Response of Continuous Systems Design of Structures for Random Excitations Nonstationary Response Nonlinear Random Vibration Appendix A: Fast Fourier Transform (FFT) in Random Vibration Appendix B: Synthesis of a Sample Function by a Monte Carlo Simulation References Index.

Long memory time series models

Abstract: For a long time the most frequently used models in time series analysis were the AR, MA and ARMA processes. Their spectral densities are continuous and therefore bounded functions on [ — n, it]. If the periodogram of real data reached significantly high values, it was considered as an indication of the trend or of a periodic component. The bias arising after trend removal in the spectral density estimators was corrected using special factors (see [7] and [19]). However, the statistical analysis of many hydrological time series has led in the last time to the conclusion that the peak of the periodogram near to the origin should be rather explained by a model with a spectral density, which is not bounded in the neighbourhood of the zero frequency. From this reason models with long memory have been investigated, because they appear to be suitable for applications of such kind. Their definition reads as follows. Let {X,} be a stationary (discrete) process with a covariance function Rk. Then {Xt} is called a process with long memory, if Y\k\ = °°In the c a s e t n a t Xli^l < °° we say that the process {X,} has short memory. From practical point of view we restrict ourselves to the processes with R0 4= 0. Then the above definitions can be formulated in the same way using the correlation function. The definition itself was proposed in [15].

Frequency and intensity noise in injection-locked semiconductor lasers: Theory and experiments

Abstract: Analytical expressions for the power spectral densities of intensity and frequency noise of single-mode semiconductor lasers operating in a regime of injection locking are derived by appropriately taking into account the spontaneous emission processes into the lasing modes of both the master and slave lasers. They show how the noise spectra of the slave are influenced by the value of the injected power, by the difference between the emission frequencies of the master and slave optical cavities, and how they are correlated to the noise properties of both the master and the free-running slave. In particular, the very low frequency part of the frequency noise of the slave turns out to coincide with that of the master within a certain frequency region whose range increases as the values of the injected signal does, too. We also present measurements of the power spectral densities obtained by means of an experimental apparatus similar to that described in [1] and show how the experimental results are accounted for by the present theory.

Frequency locking, quasiperiodicity, and chaos in extrinsic Ge

Abstract: Cooled, extrinsic GE that is voltage biased to produce a spontaneous current oscillation exhibits frequency locking, quasiperiodicity, and chaos when driven with a sinusoidal voltage. The low-frequency current power spectrum at the transition from quasiperiodic to chaotic behavior agrees in detail, both in frequency and in amplitude, with the calculated universal spectrum of the circle map. The large dynamic range (g 70 dB) and the convenient frequency (10 kHz) of the spontaneous oscillation make this an excellent system for testing the predictions of theory.

A theoretical and experimental study of angular scintillations in earth space paths

Abstract: The theoretical framework and experimental results of an antenna offsetting technique which has been used to investigate angle of arrival fluctuations in the microwave region for medium ( 30\deg ) and low elevation ( 9\deg ) angles is presented. The receiver antenna is depointed by a small angle and the antenna gain slope in dB/deg transforms angle fluctuations into amplitude fluctuations. The sensitivity and resolution of the apparatus together with the limitations due to amplitude scintillations, their time variability, and the noise floor of the system are discussed in detail. Experimental results are presented and compared with the theory developed in the paper. The study reveals that the important parameter is the product C^{2}_{n}L and values are presented and discussed. The experimental values for the root mean square (rms) angular deviation \sigma(\theta) and of the spectral density W_{\theta}(f) show a great variability between day and night and between winter and summer with values of \sigma(\theta) ranging from below 1 mdeg up to 20 mdeg. Low elevation studies at 9\deg indicate angular scintillations less intense than expected, and never exceeding 4 mdeg.

The influence of earthquakes on the Chandler wobble during 1977–1983

Abstract: Variations in the Chandler wobble's excitation function are examined in order to study the effect of 1287 earthquakes on the Chandler wobble. The computation of the moment tensor data using the centroid-moment tensor solution technique is described. An excitation function is calculated from the moment tensor data and compared to an observed excitation function derived from the polar motion observations of Gross and Chao (1985). It is observed, based on the power spectrum of the earthquake excitation function, that the earthquakes' static deformation fields have little influence on the Chandler wobble during 1977-1983.

Choice of norm for the density distribution of the Earth

Abstract: Summary. The determination of the density distribution of the Earth from gravity data is called the inverse gravimetric problem. A unique solution to this problem may be obtained by introducing a priori data concerning the covariance of density anomalies. This is equivalent to requiring the density to fulfil a minimum norm condition. The generally used norm is the one equal to the integral of the square of the density distribution (L2-norm), the use of which implies that blocks of constant density are uncorrelated. It is shown that for harmonic anomalous density distributions this leads to an external gravity field with a power spectrum (degree-variances) which tends too slowly to zero, i.e. implying gravity anomalies much less correlated than actually observed. It is proposed to use a stronger norm, equal to the integral of the square sum of the derivatives of the density distribution. As a consequence of this, base functions which are constant within blocks, are no longer a natural choice when solving the inverse gravimetric problem. Instead a block with a linearly varying density may be used. A formula for the potential of such a block is derived.

Non-invasive blood flow measurements utilizing autoregressive analysis with averaged reflection coefficients

Abstract: A system for non-invasively determining the amount of blood flow within an internal patient blood vessel by performing an autoregressive analysis of Doppler shifted acoustical signals resulting from the reflection of ultrasonic signals due to blood cell movement by averaging the reflection coefficients and residual energy levels resulting from the autoregressive analysis over a number of cardiac cycles. Each cardiac cycle is determined by an analysis of the patient's electrocardiogram signals, and the resulting cardiac cycles are divided into a predefined number of time segments or channels. An autoregressive analysis is then performed on each individual channel to determine the reflection coefficients and the residual energy level for each channel. The reflection coefficients and residual energy level for each particular channel are then averaged over all the cardiac cycles to obtain an averaged reflection coefficient and averaged residual energy level for each combined channel. The power spectrum for each combined channel is then calculated from the averaged reflection coefficients and averaged residual energy level and displayed on a channel-by-channel basis utilizing different colors to represent the different power levels. The utilization of different colors greatly enhances the usability of the display by medical personnel making diagnostic decisions regarding the amount of blood flow.

Temperature dependence of noise processes in metals.

Abstract: Here we consider the analysis of the temperature and frequency dependences of the power spectral density ${S}_{V}$(f,T) of excess low-frequency noise. Two limiting cases that arise naturally from a superposition of thermally activated relaxation processes are investigated. The Lorentzian spectra associated with various relaxation times \ensuremath{\tau}=${\ensuremath{\tau}}_{0}$${e}^{E/\mathrm{kT}}$ are supposed to arise from either (i) a distribution D(E) of activation energies E (invoked in the Dutta-Horn model), or (ii) a distribution H(${\ensuremath{\tau}}_{0}$) of prefactors ${\ensuremath{\tau}}_{0}$ (as required for activated diffusion processes). Much can be learned from the analysis of noise spectra with distinctive spectral features or known temperature-dependent variance 〈\ensuremath{\delta}${V}^{2}$(T)〉, as the analysis of noise from ${\mathrm{H}}^{+}$ diffusion in Nb films has illustrated. In the absence of such distinguishing features or independent data, particularly with 1/f noise, we find that there is generally insufficient information to distinguish even these limiting models, much less to determine their parameters. We have analyzed the resistance fluctuations of small-metallic-film conductors. We find that existing 1/f noise data from noble metals can be fit by either model with a wide range of assumptions about the variance 〈\ensuremath{\delta}${V}^{2}$(T)〉. In contrast new 1/f noise data from Cr films are inconsistent with either model unless strong ad hoc temperature-dependent variance is postulated.

Roughness Measurement of X-Ray Mirror Surfaces

Abstract: In order to fabricate an X-ray mirror telescope, we investigated the roughness of mirror surfaces using X-ray scattering. With Al-K (8.34A) X-rays we measured the scattering profiles of plate glass. The spectral structure of surface roughness was revealed by the angular distribution of the X-ray scattering. The power spectral density functions of the surface-height distribution for these materials (except for a gold evapolated surface) were represented by the power-law spectra with power indices ranging from -1 to -2. The rms heights were derived to be 1.8-8.3A for a wavelength range as expected from the power-law spectrum. The results obtained with this method were found to be consistent with those with an ordinary optical profilometer.

Performance of a Discrete Spectral Peak Frequency Estimator for Doppler Wind Velocity Measurements

Abstract: A frequency estimator formed from the peak of a discrete power spectrum is examined. Expressions to compute the performance of the estimator as a function of input signal bandwidth and signal-to-noise ratio are developed and used to study the estimator's capability to measure signal mean frequencies for remote Doppler measurement of atmospheric winds. Performance comparisons with the widely used complex-covariance estimator, based on simulations, show that frequency estimates formed from the spectral peak tend to have larger variance, except in the case of narrow-band input signals where the estimate standard deviation approaches that of the complex-covariance estimator.

Contribution to the space–time study of stellar speckle patterns

Abstract: The temporal behavior of stellar speckle patterns is statistically analyzed. The time-only power spectrum is shown to be the sum of two exponentially decreasing functions defining two characteristic time constants. The corresponding correlation is the sum of two Lorentzian functions. This is consistent with the first-order expansion of the power spectrum deduced from the multiple-layer model for atmospheric turbulence. However, this model fails to account for the experimental data that show a strong correlation between the spatial structure of a speckle pattern and its temporal behavior. This leads to the introduction of a new empirical model, called the randomly jittered speckle pattern model, which gives a preponderant place to image motion. The speckle lifetime then appears to be substantially longer than the corresponding measured time constant. As a consequence, a preliminary compensation of the image motion appears to be particularly interesting in speckle interferometry or active optics experiments.

A numerical study of waves reflected from a turbulent ionosphere

Abstract: The phase screen-diffraction layer method is a powerful tool to study the signal scintillation of a wave propagating in a turbulent, stratified medium. Under the forward scattering approximation, the complex amplitude is shown to satisfy a parabolic equation which describes effects arising from phase changes due to irregularities and diffraction due to phase mixing. Below the turning point, these two effects can be computed sequentially. Stepping in altitude, phase changes are imbeded into each phase screen; diffraction between phase screens is accomplished using FFT techniques. This method is equivalent to the split-step algorithm known in ocean acoustics but generalized to the case of oblique incidence. Near the turning point, the diffraction effects are assumed negligible due to the small vertical thickness of the considered region. The deterministic part of the wave fields is taken to be proportional to the Airy functions. This allows a more accurate evaluation of the phase change near the turning point than the WKB solutions. The coupling between the ascending and descending wave is discussed. The simulation model is described and, as an example, results for a linearly stratified turbulent ionosphere are given, including statistics of the reflected wave such as power spectrum, scintillation index and spatial correlation.

Power Spectrum Representation for Nonstationary Random Vibration

Abstract: A unified theory for the power spectral representation of nonstationary random processes is presented. The principal properties of two time-dependent spectrum definitions, the physical spectrum and the instantaneous spectrum, are reviewed with emphasis placed on difficulties brought about by the uncertainty principle. The exact relationship between these two spectrum definitions is shown to be, in a certain sense, a generalization to nonstationary processes of the Wiener-Khintchine theorem. Expressions for the physical and instantaneous spectra of a pair of beating sinusoids are derived, plotted, and discussed in relation to the uncertainty principle. Simple, general expressions for the instantaneous and physical spectra of the uniformly modulated process and for the mean-square system response to the uniformly modulated process are derived and discussed.

Second- and Fourth-order Statistics of Doubly Scattered Speckle

Abstract: The statistics of doubly scattered laser speckle, in which the size of the diffracting aperture is arbitrary relative to the spatial scales of the incident random field and the random diffuser in the aperture, is studied. The diffracted amplitude of the combined speckle and diffuser fields (both of which are spatially stationary) is shown to be non-stationary. A further spatial averaging can be carried out to yield an intensity correlation function (termed the asymptotically stationary intensity correlation function) which depends upon a single spatial variable and thus possesses a power spectrum. Numerical calculations are carried out for representative situations, and their physical interpretations are discussed.

Gaussian white-noise generation for digital signal synthesis

Abstract: An algorithm for simulating a random Gaussian noise signal on a computer is proposed. The power spectrum of the generated signal is constant, and the ordinates of the phase spectrum are independent and uniformly distributed. A computer program has been developed based on this algorithm and used with a signal generator to test electronic systems.

System for detecting the presence of a signal of a particular data rate

Abstract: A multiple data rate detector which examines the power spectral density of the received signal and thereby determines whether the signal is wihtin one of N known data rate ranges. The invention includes a first filter, with a first passband and a second filter having a second distinct passband. First and second power detectors are provided for detecting the power associated with the output of the first and second filters. The outputs of the power detectors are compared to yield a signal indicative of the data rate.

Measurement of roughness properties of diamond-turned metal surfaces using light-scattering method

Abstract: The roughness parameters of diamond-turned metal surfaces are obtained from the Fourier transform of the scattered light intensity. Theoretical consideration of the scattered light intensity and its Fourier transform is made. Under the condition of weak scattering, the Fourier transform of the scattered intensity is equivalent to the autocorrelation of the surface. From this autocorrelation function, we can derive the parameters of the surface roughness, namely, the amplitude and frequency of the periodic tool marks and the rms roughness and correlation length of the random surface component. The surface-roughness parameters of the diamond-turned surfaces of aluminum alloy are determined experimentally from the autocorrelation function. The data obtained by light scattering are compared with those of the conventional stylus method. They show qualitative agreement.