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A crosscorrelation method of measuring the impulse response of linear systems is presented. The technique, implementation, and limitations of this method are discussed. A simple system is designed and built using discrete components and the impulse response of a linear circuit is measured. Theoretical and software simulation results are presented.
Data processing by cross correlation techniques to decode PFM signals from IMP satellites
Some results of a study of the importance of geometrical features of the combustor to combustion roughness and resulting noise are presented. Comparison is made among a perforated can flame holder, a plane slotted flame holder and a plane slotted flame holder which introduces two counter swirling streams. The latter is found to permit the most stable, quiet combustion. Crosscorrelations between the time derivative of chamber pressure fluctuations and far field noise are found to be stronger than between the far field noise and the direct chamber pressure signal. Temperature fluctuations in the combustor nozzle are also found to have a reasonably strong crosscorrelation with far field sound.
We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment of phases in the nonlinear regime. We also report on the accuracy of particle positions and velocities produced by TZA.
The proposed project was a continuation of our work on the spectral evolution of gamma-ray bursts begun when the Co-I on this proposal. Lyle Ford, was my graduate student. In the proposal we discussed two projects. The first was finishing and publishing the last chapter of Professor Ford's thesis. In this research effort we looked for correlations in the energies of pairs of counts recorded by the BATSE Spectroscopy Detectors within a short time of each other. A greater correlation within a short time would indicate that the observed broadband spectrum is really composed of narrowband spectral components which last for a short time and which rapidly sum to the observed spectrum. We did not find any evidence for such narrowband emission, and are setting limits on its presence. Professor Ford is revising the last chapter of his thesis for publication with my participation. The second project was a continuation of my study of the cross-correlations between the gamma-ray burst lightcurves in different energy bands. I published a first study with this technique (1997. Ap.J., 486, 928) which showed that "hard-to-soft" spectral evolution is prevalent both within and between the bursts' intensity spikes. I proposed to continue developing this technique. However, I have been somewhat disillusioned about using this methodology quantitatively since it averages the spectral evolution on a given timescale over the entire burst. Nonetheless, I have been applying the technique to new bursts which are scientifically interesting for other reasons. Attached I include the cross-correlations for the burst GRB 990123, the burst during which ROTSE discovered an optical transient. The solid curve is the autocorrelatl'on of BATSE's channel 3 (100-300 keV), while the dashed, dot-dashed and 3 dots-dashed curves are the crosscorrelations of channel 3 with channels 1 (25-50 keV), 2 (50-100 keV), and 4 (300-2000 keV). The order of, and separation between, the curves on the positive lag side indicate "hard-to-soft" evolution on all timescales, while the FWHM of the crosscorrelations shows that the intensity spikes are narrower at high energy than at low energy. I have also been participating with my colleague on the BATSE team on other spectral evolution studies. Note that while I continue as a member of the BATSE team, I no longer receive funding from the team. For example, Preece et al. (1998, Ap.J., 496, 849) showed that the high energy spectral index varies during a burst, usually following a "hard-to-soft" trend. In addition, we have just submitted a catalog (Preece et al. 1999, Ap. J., submitted) of time-resolved spectral fits.
We developed a picosecond photodetector based on our Bridgman-grown and specially engineered cadmium magnesium telluride (Cd 1–x MgxTe) single crystal that is sensitive to both optical and X-ray pulses for coarse timing in free-electron laser applications. Cd 1–x MgxTe is a widebandgap semiconductor with potential applications, not only in optoelectronics, but also in particle physics as an intense pulse radiation detector for bremsstrahlung, X-ray/gamma-ray radiation, thermal neutrons, and medical imaging. For femtosecond optical and X-ray crosscorrelation, the material must have a very short lifetime, a condition that is opposite to that required for nuclear spectroscopy applications. At the same time, the material also needs to have a very low bulk leakage current, in the 10–90 nA range for voltages to even 1000 V. Hence, the ability to tailor or engineer the material is very crucial. Picosecond response and the crystal growth of this specially engineered Cd 1–x MgxTe material are presented. Furthermore, other characterization and transient measurements are discussed along with room-temperature semiconductor detector performance for other nuclear radiation detection applications.
Envelope polarity coincidence crosscorrelator for detection and identification problems involving weak wideband microwave signals
A noise model is formulated to describe the impulse noise in many digital systems. A simplified model, which assumes that each noise burst contains a randomly weighted version of the same basic waveform, is used to derive the performance equations for a correlation receiver. The expected number of bit errors per noise burst is expressed as a function of the average signal energy, signal-set correlation coefficient, bit time, noise-weighting-factor variance and probability density function, and a time range function which depends on the crosscorrelation of the signal-set basis functions and the noise waveform. A procedure is established for extending the results for the simplified noise model to the general model. Unlike the performance results for Gaussian noise, it is shown that for impulse noise the error performance is affected by the choice of signal-set basis functions and that Orthogonal signaling is not equivalent to On-Off signaling with the same average energy.
The performance of a path diversity satellite-to-ground millimeter wave link with two ground terminals separated by 4 km is discussed. At this separation distance the duration of fades below 6 dB was decreased by at least a factor of 10 when using path diversity and the cumulative crosscorrelation between the attenuations observed at the two terminals during rain events was approximately 0.45. Narrow beam radiometers directed along the propagation paths were also utilized to relate the path radiometric temperature to the path attenuation. An analysis of downlink propagation data for generating diversity link performance statistics is included.
The machine processing is discussed of spatially variant multitemporal data such as imagery obtained at different times which requires that these data be in geometrical registration so that the analysis processor may obtain the datum for a specified ground resolution element in each of the sets of imagery being utilized for analysis. Misregistration between corresponding subsets of imagery contains both a displacement and a geometrical distortion component. Search techniques utilizing the moduli of the Fourier Transforms are developed for estimating the coefficients of geometrical distortion components of this model. Following the correction of these distortion components, the displacement is located by the crosscorrelation of a template obtained from one set of data, termed the reference, with the second, or background data. This template, derived for the optimum discrimination of the reference data embedded in the background, is determined by the solution of a system of equations involving the reference data and the covariance matrix of these data.
Preliminary experimental data on the effectiveness of conventional radars in measuring the movement and evolution of meteorological echoes when the radar is connected to a programmable real-time processor are examined. In the processor programming is accomplished by conceiving abstract machines which constitute the actual programs used in the methods employed. An analysis of these methods, such as the center of gravity method, the contour-displacement method, the method of slope, the cross-section method, the contour crosscorrelation method, the method of echo evolution at each point, and three-dimensional measurements, shows that the motions deduced from them may differ notably (since each method determines different quantities) but the plurality of measurement may give additional information on the characteristics of the precipitation.
An impulse noise model, which assumes that each noise burst contains a randomly weighted version of a basic waveform, is used to derive the performance equations for a correlation receiver. The expected number of bit errors per noise burst is expressed as a function of the average signal energy, signal-set correlation coefficient, bit time, noise-weighting-factor variance and probability density function, and a time range function which depends on the crosscorrelation of the signal-set basis functions and the noise waveform. Unlike the performance results for additive white Gaussian noise, it is shown that the error performance for impulse noise is affected by the choice of signal-set basis function, and that Orthogonal signaling is not equivalent to On-Off signaling with the same average energy. Furthermore, it is demonstrated that the correlation-receiver error performance can be improved by inserting a properly specified nonlinear device prior to the receiver input.
Several approaches to the problem of determining the far field directivity of an acoustic source located in a reverberant environment, such as a wind tunnel, are investigated analytically and experimentally. The decrease of sound pressure level with distance is illustrated; and the spatial extent of the hydrodynamic and geometric near fields, the far field, and the reverberant field are described. A previously-prosposed analytical technique for predicting the far field directivity of the acoustic source on the basis of near field data is investigated. Experiments are conducted with small acoustic sources and an analysis is performed to determine the variation with distance from the source of the directionality of the sound field. A novel experiment is conducted in which the sound pressure measured at various distances from an acoustic driver located in the NASA Ames 40 x 80 ft wind tunnel is crosscorrelated with the driver excitation voltage.
The autocorrelation and crosscorrelation properties of pseudorandom (PN) sequences are analyzed by using some important properties of PN sequences. These properties make this discussion understandable without the need of linear algebraic approach. The analysis is followed by some experimental results.
Magnetograms made at Mt. Wilson Observatory from January 1967 to May 1982 are crosscorrelated in 34 latitude strips at 1-4-day increments to determine the rotation of magnetic features in the solar photosphere. The data are smoothed by averaging corresponding correlations and calculating rotation from the displacement of the averaged-correlation maximum; the usefulness and validity of this procedure are discussed. No significant time variation or field dependence is found for the period of the observations, at least to the accuracy of the calculated means (variance of from about 2 m/sec at low latitudes to about 10 m/sec near the poles). The rotation function omega at solar latitude phi is shown to be 2.902 0.464 sin sq phi - 0.328 sin to the 4th phi microrad/sec, in agreement with the Mt. Wilson Doppler profile near the poles and with the sunspot determination of Newton and Nunn (1951) at sunspot latitudes, where the Doppler estimate is about 30 m/sec slower.
Potential tests using turbulence velocity histories measured in the SPAN-MAT Program are outlined to determine validity of the homogeneous, momentarily frozen assumptions for the vertical turbulence velocity component and the homogeneous, isotropic, momentarily frozen assumptions for the horizontal turbulence velocity components. In addition, methods are reviewed for prediction of the crosscorrelation function between any two spatially separated turbulence velocity components using the homogeneous, isotropic, momentarily frozen assumptions and measurements of the transverse and longitudinal turbulence velocity components.
The temporal correlations of continuum and broad emission-line fluxes from the Seyfert galaxy NGC 5548 as measured during the 1989 monitoring campaign show two related peculiarities: first, some of the crosscorrelations of line and continuum flux appear steeper on the negative time lag side than the continuum autocorrelation itself; then, the autocorrelation of the line flux is sometimes more sharply peaked than the continuum autocorrelation function. These are here interpreted as evidence that conditions in the inner part of the broad-line region are such that some emission lines decrease in intensity as the continuum strengthens.
A full custom, 25 MHz, 1.6 microns CMOS Correlator chip is presented. The 5.15mm by 4.23mm chip performs either autocorrelation or crosscorrelation, consuming less than 10mW per channel. The correlator, designed for a space borne spectrometer, contains 32 channels. The 24 bit accumulator registers can be read independent of the input data path, in either 8 bit bytes, or 16 bit words. The device is cascadable and allows integration periods of up to 1.78 seconds, at 25 Megasamples/second. The controllers, for the input data path and the data output section, are implemented with Sequence Invariant State Machines.