Weighted Wavelet Z-transform Research Articles

Periodic radio variability in NRAO 530: phase dispersion minimization analysis

A periodicity analysis of the radio light curves of the blazar NRAO 530 at 14.5, 8.0, and 4.8 GHz is presented employing an improved phase dispersion minimization technique. The result, which shows two persistent periodic components of ∼ 6 and ∼ 10 yr at all three frequencies, is consistent with the results obtained with the Lomb-Scargle periodogram and weighted wavelet Z-transform algorithms. The reliability of the derived periodicities is confirmed by the Monte Carlo numerical simulations which show a high statistical confidence. (Quasi-)Periodic fluctuations of the radio luminosity of NRAO 530 might be associated with the oscillations of the accretion disk triggered by hydrodynamic instabilities of the accreted flow.

WWZ Analysis on the Variability Data of Quasar 3C 345

A new method to analyze unevenly-spaced data is described. It is based on the principle of wavelet analysis and called the weighted wavelet Z-transform (WWZ). Rather complete optical B-band data of the quasar 3C 345 in more than 100 years are collected to obtain its long-term light curve. With the WWZ method, the variability data from 1965 to 1992 are analyzed. The result shows that the data contain 3 periodical components, in which the periodicity of T = 4.54 ∼ 5.23 yr and T = 9.59 ∼ 11.51 yr is steady, while T = 624 ∼ 941 d is not a steady period.

Enhanced Rieger type periodicities' detection in X-ray solar flares and statistical validation of Rossby waves' existence

AbstractThe known Rieger Periodicity (ranging in literature from 150 up to 160 days) is obvious in numerous solar indices. Many sub-harmonic periodicities have also been observed (128–, 102–, 78–, and 51 – days) in flare, sunspot, radio bursts, neutrino flux and flow data, coined as Rieger Type Periodicities (RTPs). Several attempts are focused to the discovery of their source, as well as the explanation of some intrinsic attributes that they present, such as their connection to extremely active flares, their temporal intermittency as well as their tendency to occur near solar maxima. In this paper, we link the X-ray flare observations made on Geosynchronous Operational Environmental Satellites (GOES) to an existing theoretical model (Lou 2000), suggesting that the mechanism behind the Rieger Type Periodicities is the Rossby Type Waves. The enhanced data analysis methods used in this article (Scargle-Lomb periodogram and Weighted Wavelet Z-Transform) provide the proper resolution needed to argue that RTPs are present also in less energetic flares, contrary to what has been inferred from observations so far.

Enhanced Rieger-type periodicities' detection in X-ray solar flares and statistical validation of Rossby waves' existence

The known Rieger periodicity (ranging in literature from 150 up to 160 d) is obvious in numerous solar indices. Many subharmonic periodicities have also been observed (128-, 102-, 78- and 51-d) in flare, sunspot, radio bursts, neutrino flux and flow data, coined as Rieger-type periodicities (RTPs). Several attempts are focused to the discovery of their source, as well as the explanation of some intrinsic attributes that they present, such as their connection to extremely active flares, their temporal intermittency as well as their tendency to occur near solar maxima. In this paper, we link the X-ray flare observations made on Geosynchronous Operational Environmental Satellites (GOES) to the already existing theoretical Lou model, suggesting that the mechanism behind the RTPs is the Rossby-type waves. The enhanced data analysis methods used in this article (Scargle-Lomb periodogram and Weighted Wavelet Z-Transform) provide the proper resolution needed to argue that RTPs are present also in less energetic flares, contrary to what has been inferred from observations so far.

웨이블렛을 이용한 ∈ AURIGAE SYSTEM 주성 F별의 주기분석

이 연구에서는 장주기 변광쌍성 <TEX>${\in}$</TEX> Aurigae의 주성에 대한 측광 관측자료를 바탕으로 그 별의 변광주기를 분석하였다. 이를 위하여 1842년부터 2006년까지 약 160여년에 걸쳐서 여러 관측소에서 관측된 자료를 이용하였다. 식 바깥 부분의 자료를 선별하여 CLEANest와 Wavelet 알고리즘으로 주기를 분석한 결과 <TEX>${\in}$</TEX> Aurigae의 주성 F별은 시간에 따라서 진폭이 변하기는 하지만 몇개의 특정 주파수가 일정하게 유지되는 진동 특성을 가지고 있음을 알 수 있었다. 특히 두 개의 주기(67일과 123일)가 지속적으로 나타난 것은 지금까지 부분적으로 주기를 구하였던 결과에서 주기가 시간에 따라서 불규칙하게 변한다고 판단되어졌던 것과는 달리 <TEX>${\in}$</TEX> Aurigae의 주성이 이중 모드 또는 다주기적 변광을 하고 있다는 것을 말해준다고 하겠다. 이는 <TEX>${\in}$</TEX> Aurigae의 주성이 post-AGB의 단계에 있다기 보다는 질량이 큰 초거성 상태임을 암시하는 결과라고도 할 수 있다. 또한 황색 초거성의 변광기작에 대해 명확하게 이해되지 못하고 있는 현재의 입장에서 <TEX>${\in}$</TEX> Aurigae의 식 바깥부분에서의 추가적인 관측이 필요함을 논의하였다. We present a detailed period analysis for the F-type primary of <TEX>${\in}$</TEX> Aurigae by means of Fourier and wavelet algorithm. After collecting all available data which have been observed for around 160 years (1842 - 2006) from various international databases and published references we selected only data obtained during outside eclipse among them again. As a result of analysis using CLEANest and WWZ(weighted wavelet Z-transform) several frequencies including two clear periods (<TEX>$67^d\;and\;123^d$</TEX>) were found. In contrast to previous results that the periods vary irregularly it seems that the primary of <TEX>${\in}$</TEX> Aurigae is double mode or multiperiodic pulsator. The presence of the two periods and their ratio indicates that the high-mass interpretation of the variable could be valid. Also better understanding of the mechanisms driving the light variability of F-type supergiant stars requires continual series of photometric and radial velocity measurements in outside eclipse of this star.

Wavelet analysis of hydrological and water quality signals in an agricultural watershed

Studying temporal patterns of hydrology and water quality can assist in understanding hydrological processes, improving hydrological modeling, and water quality monitoring. Using wavelet analysis, we analyzed temporal patterns of three hydrological signals (precipitation, stream flow, and well water level) for three periods (15 years, 3 year, and a hydrological year). For three unevenly sampled water quality signals (nitrate, chloride, and sodium), the weighted wavelet Z-transform (WWZ) method was employed. The results showed that the wavelet analysis of hydrological signals showed advantages of detecting detailed temporal patterns compared to the classical Fourier analysis. No strong temporal pattern of precipitation was found for all three periods. For the 15 years' continual monitoring datasets, strong consistent annual temporal pattern of well water level and an intermittent annual temporal pattern of stream flow were observed. For the relative short-time periods (three years and a hydrological year), strong seasonal patterns of stream flow and well water level were noticed. Using the WWZ method, seasonal patterns of the three stream water quality indicators can be associated with their seasonal shifts. Nitrate concentration showed stronger temporal patterns than chloride and sodium over longer time periods (15 and 3 years). In a hydrological year, temporal patterns of nitrate, chloride, and sodium shared some similarities as well as dissimilarities, as can be explained by their different transport pathways and sources. Sodium and chloride peak concentrations in the winter season were captured by the wavelet analysis. It is concluded that wavelet analysis can be a useful tool to analyze detailed temporal patterns of non-stationary hydrological and water quality signals over different temporal scales.

Detection of phase disturbances of free core nutation of the Earth and their concurrence with geomagnetic jerks

Abstract We detected phase disturbances of the Free Core Nutation (FCN) of the Earth directly from the analysis of the Very Long Baseline Interferometer (VLBI) observation of the Earth rotation for the period 1984–2003 by applying the Weighted Wavelet Z-Transform (WWZ) method and the Short-time Periodogram with the Gabor function (SPG) method. During the period, the FCN had two significant phase disturbances in 1992 and 1998. These epochs coincide with the reported occurrence of geomagnetic jerks.

Wavelets for period analysis of unevenly sampled time series

The wavelet transform shows great promise as a method for period analysis in time series, particularly for detecting the time evolution of the parameters (period, amplitude, phase) describing periodic and pseudo-periodic signals. However, when applied to unevenly sampled time series, the response of the wavelet transform is often more dependent on irregularities in the number and spacing of available data than on actual changes in the parameters of the signal. Yet by casting the wavelet transform as a projection, we can derive its statistical behavior and devise advantageous rescaled transforms. By treating it as a weighted projection to form the weighted wavelet Z-transform (WWZ), we improve its ability to detect, and especially to quantify, periodic and pseudo-periodic signals. The methods are illustrated by analysis of artificial test data, and of the light curves of the variable stars R Aquila and FS Comae.