Nonparametric time series analysis for periodically correlated processes

Hurd, Harry L.

doi:10.1109/18.32129

Cited by 95 publications

(55 citation statements)

References 13 publications

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“…Since the Fourier transforms of u and v are both linear combinations of nine Dirac delta functions centered on the frequencies ±l Ω , l = 0, 1, 2, 3, 4 (see equations (27)(28)(29)(30) in reference [8] for the expressions of u and v), it follows thatX GW (0) (ω) is also a linear combination of Dirac delta functions. In particular, in the limit of negligible Doppler modulation, the resulting expression (14) reduces as expected to that of a purely amplitude modulated sinusoidal signal with central frequency equal to ω s and upper and lower band-limits given by ω s + 4Ω and ω s − 4Ω respectively [24].…”

Section: A the Fourier Transform Of A Binary Signalmentioning

confidence: 99%

“…Their analytic expressions are given in equations (41-44) of reference [8], while the functions u k (t), and v k (t) (k = 2, 3) are given in equations (27,28) in the same reference.…”

Section: The Lisa Response To Signals From Binary Systemsmentioning

confidence: 99%

“…These kind of processes have been studied for many years, and are usually referred to as cyclostationary random processes (see [27] for a comprehensive overview of the subject and for more references). In what follows we will briefly summarize the properties of cyclostationary processes that are relevant to our problem.…”

Section: Cyclostationary Processesmentioning

confidence: 99%

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White-dwarf–white-dwarf galactic background in the LISA data

et al. 2005

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LISA (Laser Interferometer Space Antenna) is a proposed space mission, which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. In the low-part of its frequency band, the LISA strain sensitivity will be dominated by the incoherent superposition of hundreds of millions of gravitational wave signals radiated by inspiraling white-dwarf binaries present in our own galaxy. In order to estimate the magnitude of the LISA response to this background, we have simulated a synthesized population that recently appeared in the literature. Our approach relies on entirely analytic expressions of the LISA Time-Delay Interferometric responses to the gravitational radiation emitted by such systems, which allows us to implement a computationally efficient and accurate simulation of the background in the LISA data. We find the amplitude of the galactic white-dwarf binary background in the LISA data to be modulated in time, reaching a minimum equal to about twice that of the LISA noise for a period of about two months around the time when the Sun-LISA direction is roughly oriented towards the Autumn equinox. This suggests that, during this time period, LISA could search for other gravitational wave signals incoming from directions that are away from the galactic plane. Since the galactic white-dwarfs background will be observed by LISA not as a stationary but rather as a cyclostationary random process with a period of one year, we summarize the theory of cyclostationary random processes, present the corresponding generalized spectral method needed to characterize such process, and make a comparison between our analytic results and those obtained by applying our method to the simulated data. We find that, by measuring the generalized spectral components of the white-dwarf background, LISA will be able to infer properties of the distribution of the white-dwarfs binary systems present in our Galaxy.

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Section: A the Fourier Transform Of A Binary Signalmentioning

confidence: 99%

“…Their analytic expressions are given in equations (41-44) of reference [8], while the functions u k (t), and v k (t) (k = 2, 3) are given in equations (27,28) in the same reference.…”

Section: The Lisa Response To Signals From Binary Systemsmentioning

confidence: 99%

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White-dwarf–white-dwarf galactic background in the LISA data

et al. 2005

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“…The special case with a = 1 was considered in Hurd (1989) and Dandawate and Giannakis (1994). Because of the symmetries in the case of a real-valued process, if u =ai; + £isalineof spectral support, then so are u = a~lv -a~lb, u-av -b and u = a~lv +a~lb with…”

Section: Allmentioning

confidence: 99%

“…In recent years there has been growing interest in the spectral analysis of various specific models of nonstationarity. A class of models of this type that have generated considerable interest are the periodically correlated (or cyclostationary, periodically stationary) or almost periodically correlated processes [Alekseev (1988), Hurd (1989), Gardner (1991), Allen (1994a, 1994b), Dandawate and Giannakis (1994) and Leskow and Weron (1992)]. The stationary and almost periodically correlated processes are proper subsets of the class of harmonizable processes.…”

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confidence: 99%

Spectral Analysis for Harmonizable Processes

Lii

Rosenblatt

2011

Selected Works of Murray Rosenblatt

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Spectral estimation of nonstationary but harmonizable processes is considered. Given a single realization of the process, periodogram-like and consistent estimators are proposed for spectral mass estimation when the spectral support of the process consists of lines. Such a process can arise in signals of a moving source from array data or multipath signals with Doppler stretch from a single receiver. Such processes also include periodically correlated (or cyclostationary) and almost periodically correlated processes as special cases. We give detailed analysis on aliasing, bias and covariances of various estimators. It is shown that dividing a single long realization of the process into nonoverlapping subsections and then averaging periodogramlike estimates formed from each subsection will not yield meaningful results if one is estimating spectral mass with support on lines with slope not equal to 1. If the slope of a spectral support line is irrational, then spectral masses do not fold on top of each other in estimation even if the data are equally spaced. Simulation examples are given to illustrate various theoretical results.

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References

2012

Generalizations of Cyclostationary Signal Processing

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Nonparametric time series analysis for periodically correlated processes

Cited by 95 publications

References 13 publications

White-dwarf–white-dwarf galactic background in the LISA data

White-dwarf–white-dwarf galactic background in the LISA data

Spectral Analysis for Harmonizable Processes

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