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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data

This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the cross-correlation function (CCF) of time series which are not evenly sampled. The series may consist of quantized point data (e.g., yes/no processes such as photon arrival). The DFT, which can be inverted to recover the original data and the sampling, is used to compute correlation functions by means of a procedure which is effectively, but not explicitly, an interpolation. The CCF can be computed for two time series not even sampled at the same set of times. Techniques for removing the distortion of the correlation functions caused by the sampling, determining the value of a constant component to the data, and treating unequally weighted data are also discussed. FORTRAN code for the Fourier transform algorithm and numerical examples of the techniques are given.

Scargle, Jeffrey D.↗
NASA NTRS1994

How cosmic microwave background correlations at large angles relate to mass autocorrelations in space

The Sachs-Wolfe effect is known to produce large angular scale fluctuations in the cosmic microwave background radiation (CMBR) due to gravitational potential fluctuations. We show how the angular correlation function of the CMBR can be expressed explicitly in terms of the mass autocorrelation function xi(r) in the universe. We derive analytic expressions for the angular correlation function and its multipole moments in terms of integrals over xi(r) or its second moment, J(sub 3)(r), which does not need to satisfy the sort of integral constraint that xi(r) must. We derive similar expressions for bulk flow velocity in terms of xi and J(sub 3). One interesting result that emerges directly from this analysis is that, for all angles theta, there is a substantial contribution to the correlation function from a wide range of distance r and that radial shape of this contribution does not vary greatly with angle.

Blumenthal, George R.↗
NASA NTRS2008

TDR Using Autocorrelation and Varying-Duration Pulses

In an alternative to a prior technique of time-domain-reflectometry (TDR) in which very short excitation pulses are used, the pulses have very short rise and fall times and the pulse duration is varied continuously between a minimum and a maximum value. In both the present and prior techniques, the basic idea is to (1) measure the times between the generation of excitation pulses and the reception of reflections of the pulses as indications of the locations of one or more defects along a cable and (2) measure the amplitudes of the reflections as indication of the magnitudes of the defects. In general, an excitation pulse has a duration T. Each leading and trailing edge of an excitation pulse generates a reflection from a defect, so that a unique pair of reflections is associated with each defect. In the present alternative technique, the processing of the measured reflection signal includes computation of the autocorrelation function R(tau) identical with fx(t)x(t-tau)dt where t is time, x(t) is the measured reflection signal at time t, and taus is the correlation interval. The integration is performed over a measurement time interval short enough to enable identification and location of a defect within the corresponding spatial interval along the cable. Typically, where there is a defect, R(tau) exhibits a negative peak having maximum magnitude for tau in the vicinity of T. This peak can be used as a means of identifying a leading-edge/trailing-edge reflection pair. For a given spatial interval, measurements are made and R(tau) computed, as described above, for pulse durations T ranging from the minimum to the maximum value. The advantage of doing this is that the effective signal-to-noise ratio may be significantly increased over that attainable by use of a fixed pulse duration T.

Lucena, Angel↗
NASA NTRS2019

Interference Mitigation Using Cyclic Autocorrelation and Multi-Objective Optimization

Radio frequency interference on space-to-ground communications links can degrade performance and disrupt the transfer of critical data. These interference events become increasingly likely as more users enter the spectrum, due in part to shared spectrum allocations and scheduling conflicts. If this interference could be detected and mitigated by an automated system, then link performance and reliability in these scenarios could be improved. This report describes the implementation and evaluation of an automated interference mitigation system that provides this functionality. The system uses Cyclic Autocorrelation (CAC) signal processing techniques to monitor the spectrum and detect interfering signals, and it applies a multi-objective optimization approach to mitigate interference by changing link parameters to continuously optimize the link. The implementation was evaluated to characterize its signal detection capabilities for various link qualities and to compare its link management performance to Adaptive Coding and Modulation (ACM) and Constant Coding and Modulation (CCM) when in the presence of randomized interference. In the latter evaluation, the interference mitigation system achieved the highest average throughput in each tested scenario. With these results, the proposed solution provides the groundwork for further automated link management capabilities and continued investigation into interference mitigation approaches.

Interference mitigation↗
NASA NTRS1976

Autocorrelation peaks in congruential pseudorandom number generators

The complete correlation structure of several congruential pseudorandom number generators (PRNG) of the same type and small cycle length was studied to deal with the problem of congruential PRNG almost repeating themselves at intervals smaller than their cycle lengths, during simulation of bandpass filtered normal random noise. Maximum period multiplicative and mixed congruential generators were studied, with inferences drawn from examination of several tractable members of a class of random number generators, and moduli from 2 to the 5th power to 2 to the 9th power. High correlation is shown to exist in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle length. The random noise sequences in question are required when simulating electrical noise, air turbulence, or time variation of wind parameters.

Neuman, F.↗
NASA NTRS1979

Autocorrelation in Landsat data

Many computer algorithms for the analysis of Landsat data have a statistical basis which requires that the observations comprise independent samples. Four distinct methods are employed to show that this assumption commonly is not fulfilled for these data. Each leads to a similar conclusion; the data must be sampled no closer than every 10th pixel in order to yield independent estimators. The implications of this are illustrated with a simple example.

Craig, R. G.↗
NASA NTRS1988

Autocorrelation and regularization in digital images. I - Basic theory

Spatial structure occurs in remotely sensed images when the imaged scenes contain discrete objects that are identifiable in that their spectral properties are more homogeneous within than between them and other scene elements. The spatial structure introduced is manifest in statistical measures such as the autocovariance function and variogram associated with the scene, and it is possible to formulate these measures explicitly for scenes composed of simple objects of regular shapes. Digital images result from sensing scenes by an instrument with an associated point spread function (PSF). Since there is averaging over the PSF, the effect, termed regularization, induced in the image data by the instrument will influence the observable autocovariance and variogram functions of the image data. It is shown how the autocovariance or variogram of an image is a composition of the underlying scene covariance convolved with an overlap function, which is itself a convolution of the PSF. The functional form of this relationship provides an analytic basis for scene inference and eventual inversion of scene model parameters from image data.

Jupp, David L. B.↗
NASA NTRS1989

Autocorrelation and regularization in digital images. II - Simple image models

The variogram function used in geostatistical analysis is a useful statistic in the analysis of remotely sensed images. Using the results derived by Jupp et al. (1988), the basic second-order, or covariance, properties of scenes modeled by simple disks of varying size and spacing after imaging into disk-shaped pixels are analyzed to explore the relationship betwee image variograms and discrete object scene structure. The models provide insight into the nature of real images of the earth's surface and the tools for a complete analysis of the more complex case of three-dimensional illuminated discrete-object images.

Jupp, David L. B.↗
NASA NTRS1990

Constraints on large-scale clustering from the autocorrelation properties of the X-ray background

Expectations for the angular correlation function of intensity fluctuations of the extragalacitc 2-10 keV X-ray background are discussed in relation to the two-point spatial correlation functions, xi(r), of X-ray sources. A simple analytic formula for the amplitude of intensity correlations, Gamma(theta), holding in the low-redshift, small-separation approximation, is derived. The HEAO 1 A-2 upper limits on Gamma(theta) have been exploited to derive constraints on the local xi(r) functions of rich clusters of galaxies, of AGNs, and on the AGN-cluster cross-correlation, as well as on evolution of the correlation functions with cosmic time. X-ray data are found to be compatible with the Bahcall and Soneira estimates of xi(cluster-cluster) as well as with the results of recent studies of quasar clustering.

De Zotti, G.↗