Study on period search methods of variable stars: Application to ASAS and CRTS databases

Study on variable stars is an important topic of modern astrophysics. After the invention of powerful telescopes and high resolving powered CCD’s, the variable star data is accumulating in the order of peta-bytes. The huge amount of data need lot of automated methods as well as human experts. This thesis is devoted to the data analysis on variable star’s astronomical time series data and hence belong to the inter-disciplinary topic, Astrostatistics. For an observer on earth, stars that have a change in apparent brightness over time are called variable stars. The variation in brightness may be regular (periodic), quasi periodic (semi-periodic) or irregular manner (aperiodic) and are caused by various reasons. In some cases, the variation is due to some internal thermo-nuclear processes, which are generally known as intrinsic vari- ables and in some other cases, it is due to some external processes, like eclipse or rotation, which are known as extrinsic variables. Intrinsic variables can be further grouped into pulsating variables, eruptive variables and flare stars. Extrinsic variables are grouped into eclipsing binary stars and chromospheri- cal stars. Pulsating variables can again classified into Cepheid, RR Lyrae, RV Tauri, Delta Scuti, Mira etc. The eruptive or cataclysmic variables are novae, supernovae, etc., which rarely occurs and are not periodic phenomena. Most of the other variations are periodic in nature. Variable stars can be observed through many ways such as photometry, spectrophotometry and spectroscopy. The sequence of photometric observa- xiv tions on variable stars produces time series data, which contains time, magni- tude and error. The plot between variable star’s apparent magnitude and time are known as light curve. If the time series data is folded on a period, the plot between apparent magnitude and phase is known as phased light curve. The unique shape of phased light curve is a characteristic of each type of variable star. One way to identify the type of variable star and to classify them is by visually looking at the phased light curve by an expert. For last several years, automated algorithms are used to classify a group of variable stars, with the help of computers. Research on variable stars can be divided into different stages like observa- tion, data reduction, data analysis, modeling and classification. The modeling on variable stars helps to determine the short-term and long-term behaviour and to construct theoretical models (for eg:- Wilson-Devinney model for eclips- ing binaries) and to derive stellar properties like mass, radius, luminosity, tem- perature, internal and external structure, chemical composition and evolution. The classification requires the determination of the basic parameters like pe- riod, amplitude and phase and also some other derived parameters. Out of these, period is the most important parameter since the wrong periods can lead to sparse light curves and misleading information. Time series analysis is a method of applying mathematical and statistical tests to data, to quantify the variation, understand the nature of time-varying phenomena, to gain physical understanding of the system and to predict future behavior of the system. Astronomical time series usually suffer from unevenly spaced time instants, varying error conditions and possibility of big gaps. This is due to daily varying daylight and the weather conditions for ground based observations and observations from space may suffer from the impact of cosmic ray particles. Many large scale astronomical surveys such as MACHO, OGLE, EROS, xv ROTSE, PLANET, Hipparcos, MISAO, NSVS, ASAS, Pan-STARRS, Ke- pler,ESA, Gaia, LSST, CRTS provide variable star’s time series data, even though their primary intention is not variable star observation. Center for Astrostatistics, Pennsylvania State University is established to help the astro- nomical community with the aid of statistical tools for harvesting and analysing archival data. Most of these surveys releases the data to the public for further analysis. There exist many period search algorithms through astronomical time se- ries analysis, which can be classified into parametric (assume some underlying distribution for data) and non-parametric (do not assume any statistical model like Gaussian etc.,) methods. Many of the parametric methods are based on variations of discrete Fourier transforms like Generalised Lomb-Scargle peri- odogram (GLSP) by Zechmeister(2009), Significant Spectrum (SigSpec) by Reegen(2007) etc. Non-parametric methods include Phase Dispersion Minimi- sation (PDM) by Stellingwerf(1978) and Cubic spline method by Akerlof(1994) etc. Even though most of the methods can be brought under automation, any of the method stated above could not fully recover the true periods. The wrong detection of period can be due to several reasons such as power leakage to other frequencies which is due to finite total interval, finite sampling interval and finite amount of data. Another problem is aliasing, which is due to the influence of regular sampling. Also spurious periods appear due to long gaps and power flow to harmonic frequencies is an inherent problem of Fourier methods. Hence obtaining the exact period of variable star from it’s time series data is still a difficult problem, in case of huge databases, when subjected to automation. As Matthew Templeton, AAVSO, states “Variable star data analysis is not always straightforward; large-scale, automated analysis design is non-trivial”. Derekas et al. 2007, Deb et.al. 2010 states “The processing of xvi huge amount of data in these databases is quite challenging, even when looking at seemingly small issues such as period determination and classification”. It will be beneficial for the variable star astronomical community, if basic parameters, such as period, amplitude and phase are obtained more accurately, when huge time series databases are subjected to automation. In the present thesis work, the theories of four popular period search methods are studied, the strength and weakness of these methods are evaluated by applying it on two survey databases and finally a modified form of cubic spline method is intro- duced to confirm the exact period of variable star. For the classification of new variable stars discovered and entering them in the “General Catalogue of Vari- able Stars” or other databases like “Variable Star Index“, the characteristics of the variability has to be quantified in term of variable star parameters.

Polyphase Implementation of Non-recursive Comb Decimators for Sigma-Delta A/D Converters

In a sigma-delta analog to digital (A/D) As most of the sigma-delta ADC applications require converter, the most computationally intensive block is decimation filters with linear phase characteristics, the decimation filter and its hardware implementation symmetric Finite Impulse Response (FIR) filters are may require millions of transistors. Since these widely used for implementation. But the number of FIR converters are now targeted for a portable application, filter coefficients will be quite large for implementing a a hardware efficient design is an implicit requirement. narrow band decimation filter. Implementing decimation In this effect, this paper presents a computationally filter in several stages reduces the total number of filter efficient polyphase implementation of non-recursive coefficients, and hence reduces the hardware complexity cascaded integrator comb (CIC) decimators for and power consumption [2]. Sigma-Delta Converters (SDCs). The SDCs are The first stage of decimation filter can be operating at high oversampling frequencies and hence implemented very efficiently using a cascade of integrators require large sampling rate conversions. The filtering and comb filters which do not require multiplication or and rate reduction are performed in several stages to coefficient storage. The remaining filtering is performed reduce hardware complexity and power dissipation. either in single stage or in two stages with more complex The CIC filters are widely adopted as the first stage of FIR or infinite impulse response (IIR) filters according to decimation due to its multiplier free structure. In this the requirements. The amount of passband aliasing or research, the performance of polyphase structure is imaging error can be brought within prescribed bounds by compared with the CICs using recursive and increasing the number of stages in the CIC filter. The non-recursive algorithms in terms of power, speed and width of the passband and the frequency characteristics area. This polyphase implementation offers high speed outside the passband are severely limited. So, CIC filters operation and low power consumption. The polyphase are used to make the transition between high and low implementation of 4th order CIC filter with a sampling rates. Conventional filters operating at low decimation factor of '64' and input word length of sampling rate are used to attain the required transition '4-bits' offers about 70% and 37% of power saving bandwidth and stopband attenuation. compared to the corresponding recursive and Several papers are available in literature that deals non-recursive implementations respectively. The same with different implementations of decimation filter polyphase CIC filter can operate about 7 times faster architecture for sigma-delta ADCs. Hogenauer has than the recursive and about 3.7 times faster than the described the design procedures for decimation and non-recursive CIC filters.

Wideband Low-Distortion Sigma-Delta ADC for WLAN

This work presents a wideband low-distortion sigmadelta analog-to-digital converter (ADC) for Wireless Local Area Network (WLAN) standard. The proposed converter makes use of low-distortion swing suppression SDM architecture which is highly suitable for low oversampling ratios to attain high linearity over a wide bandwidth. The modulator employs a 2-2 cascaded sigma-delta modulator with feedforward path with a single-bit quantizer in the first stage and 4-bit in the second stage. The modulator is designed in TSMC 0.18um CMOS technology and operates at 1.8V supply voltage. Simulation results show that, a peak SNDR of 57dB and a spurious free dynamic range (SFDR) of 66dB is obtained for a 10MHz signal bandwidth, and an oversampling ratio of 8.

A Multi-Mode Sigma-Delta ADC for GSM/WCDMA/ WLAN Applications

The demand for new telecommunication services requiring higher capacities, data rates and different operating modes have motivated the development of new generation multi-standard wireless transceivers. In multistandard design, sigma-delta based ADC is one of the most popular choices. To this end, in this paper we present cascaded 2-2-2 reconfigurable sigma-delta modulator that can handle GSM, WCDMA and WLAN standards. The modulator makes use of a low-distortion swing suppression topology which is highly suitable for wide band applications. In GSM mode, only the first stage (2nd order Σ-Δ ADC) is used to achieve a peak SNDR of 88dB with oversampling ratio of 160 for a bandwidth of 200KHz and for WCDMA mode a 2-2 cascaded structure (4th order) is turned on with 1-bit in the first stage and 2-bit in the second stage to achieve 74 dB peak SNDR with over-sampling ratio of 16 for a bandwidth of 2MHz. Finally, a 2-2-2 cascaded MASH architecture with 4-bit in the last stage is proposed to achieve a peak SNDR of 58dB for WLAN for a bandwidth of 20MHz. The novelty lies in the fact that unused blocks of second and third stages can be made inactive to achieve low power consumption. The modulator is designed in TSMC 0.18um CMOS technology and operates at 1.8 supply voltage

A Triple-mode Sigma-delta Modulator Design for Wireless Standards

This work presents a triple-mode sigma-delta modulator for three wireless standards namely GSM/WCDMA and Bluetooth. A reconfigurable ADC has been used to meet the wide bandwidth and high dynamic range requirements of the multi-standard receivers with less power consumption. A highly linear sigma-delta ADC which has reduced sensitivity to circuit imperfections has been chosen in our design. This is particularly suitable for wide band applications where the oversampling ratio is low. Simulation results indicate that the modulator achieves a peak SNDR of 84/68/68 dB over a bandwidth of 0.2/3.84/1.5 MHz with an oversampling ratio 128/8/8 in GSM/WCDMA/Bluetooth modes respectively

GA-based Optimization of a Fourth-order Sigma-delta Modulator for WLAN

Over-sampling sigma-delta analogue-to-digital converters (ADCs) are one of the key building blocks of state of the art wireless transceivers. In the sigma-delta modulator design the scaling coefficients determine the overall signal-to-noise ratio. Therefore, selecting the optimum value of the coefficient is very important. To this end, this paper addresses the design of a fourthorder multi-bit sigma-delta modulator for Wireless Local Area Networks (WLAN) receiver with feed-forward path and the optimum coefficients are selected using genetic algorithm (GA)- based search method. In particular, the proposed converter makes use of low-distortion swing suppression SDM architecture which is highly suitable for low oversampling ratios to attain high linearity over a wide bandwidth. The focus of this paper is the identification of the best coefficients suitable for the proposed topology as well as the optimization of a set of system parameters in order to achieve the desired signal-to-noise ratio. GA-based search engine is a stochastic search method which can find the optimum solution within the given constraints.

A Triple-Mode Feed-Forward Sigma-Delta Modulator Design For Gsm / Wcdma / Wlan Applications

This paper presents a cascaded 2-2-2 reconfigurable sigma-delta modulator that can handle GSM, WCDMA and WLAN standards. The modulator makes use of a low-distortion swing suppression topology which is highly suitable for wide band applications. In GSM mode, only the first stage (2nd order Σ-Δ ADC) is turned on to achieve 88dB dynamic range with oversampling ratio of 160 for a bandwidth of 200KHz; in WCDMA mode a 2-2 cascaded structure (4th order) is turned on with 1-bit in the first stage and 2-bit in the second stage to achieve 74 dB dynamic range with oversampling ratio of 16 for a bandwidth of 2MHz and a 2-2-2 cascaded MASH architecture with a 4-bit in the last stage to achieve a dynamic range of 58dB for a bandwidth of 20MHz. The novelty lies in the fact that unused blocks of second and third stages can be switched off taking into considerations like power consumption. The modulator is designed in TSMC 0.18um CMOS technology and operates at 1.8 supply voltage.