Time-frequency distributions for a wide-sense stationary random signal

Posch, T.E.

doi:10.1109/29.52715

Cited by 6 publications

(2 citation statements)

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“…Thus these TFR estimators, which include the CWD, the BJD and the Gabor spectrogram, are also biased, with the amount of the bias depending on the noise level. We (Posch 1990). In general, the variance of the TFR will depend on the amount of smoothing by the kernel: more smoothing results in a lower variance (Williams 1998).…”

Section: Statistical Properties Of Tfrsmentioning

confidence: 98%

“…We 1 A time series is weakly stationary if all realizations {xt} of the process {Xt} have the same mean, the (auto)covariance between any 2 samples from the same realization is a function of the time-lag between the samples only, and the variance is finite (Kendall, Stuart & Ord 1983). -27 - (Posch 1990). In general, the variance of the TFR will depend on the amount of smoothing by the kernel: more smoothing results in a lower variance (Williams 1998).…”

Section: Statistical Properties Of Tfrsmentioning

confidence: 99%

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Wavelets With Ridges: A High-Resolution Representation of Cataclysmic Variable Time Series

Blackman

2010

ApJS

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Quasi-periodic oscillations and dwarf nova oscillations occur in dwarf novae and nova-like variables during outburst and occasionally during quiescence, and have analogues in high-mass X-ray binaries and black-hole candidates. The frequent low coherence of quasi-period oscillations and dwarf nova oscillations can make detection with standard time-series tools such as periodograms problematic. This paper develops tools to analyse quasi-periodic brightness oscillations. We review the use of time-frequency representations in the astronomical literature, and show that representations such as the Choi-Williams Distribution and Zhao-Atlas-Marks Representation, which are best suited to high signal-to-noise data, cannot be assumed a priori to be the best techniques for our data, which have a much higher noise level and lower coherence. This leads us to a detailed analysis of the time-frequency resolution and statistical properties of six time-frequency representations. We conclude that the wavelet scalogram, with the addition of wavelet ridges and maxima points, is the most effective time-frequency representation for analysing quasi-periodicities in low signal-to-noise data, as it has high time-frequency resolution, and is a minimum variance estimator.We use the wavelet ridges method to re-analyse archival data from VW Hyi, and find 62 new QPOs and 7 new long-period DNOs. Relative to previous analyses, our method substantially improves the detection rate for QPOs.

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Section: Statistical Properties Of Tfrsmentioning

confidence: 98%

Section: Statistical Properties Of Tfrsmentioning

confidence: 99%