Wavelet analysis: a new significance test for signals dominated by intrinsic red-noise variability

Pawel Lachowicz

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arXiv · 0906.4176

Wavelet analysis: a new significance test for signals dominated by intrinsic red-noise variability

Pawel Lachowicz

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Abstract

We develop a new statistical test for the wavelet power spectrum. We design it with purpose of testing signals which intrinsic variability displays in a Fourier domain a red-noise component described by a single, broken or doubly-broken power-law model. We formulate our methodology as straightforwardly applicable to astronomical X-ray light curves and aimed at judging the significance level for detected quasi-periodic oscillations (QPOs). Our test is based on a comparison of wavelet coefficients derived for the source signal with these obtained from the averaged wavelet decomposition of simulated signal which preserves the same broad-band model of variability as displayed by X-ray source. We perform a test for statistically significant QPO detection in XTE J1550--564 microquasar and active galaxy of RE J1034+396 confirming these results in the wavelet domain with our method. In addition, we argue on the usefulness of our new algorithm for general class of signals displaying 1/f^alpha-type variability.

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Pawel Lachowicz. 2009-06-23. Wavelet analysis: a new significance test for signals dominated by intrinsic red-noise variability. https://arxiv.org/abs/0906.4176

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