Reliable Modeling of Ideal Generic Memristors via State-Space Transformation

The paper refers to problems of modeling and computer simulation of generic memristors caused by the so-called window functions, namely the stick effect, nonconvergence, and finding fundamentally incorrect solutions. A profoundly different modeling approach is proposed, which is mathematically equivalent to window-based modeling. However, due to its numerical stability, it definitely smoothes the above problems away

Phenomenological modelling of eclipsing system light curves

The observed light curves of most eclipsing binaries and stars with transiting planets can be well described and interpreted by current advanced physical models which also allow for the determination of many physical parameters of eclipsing systems. However, for several common practical tasks there is no need to know the detailed physics of a variable star, but only the shapes of their light curves or other phase curves. We present a set of phenomenological models for the light curves of eclipsing systems. We express the observed light curves of eclipsing binaries and stars, transited by their exoplanets orbiting in circular trajectories, by a sum of special, analytical, few-parameter functions that enable fitting their light curves with an accuracy of better than 1%. The proposed set of phenomenological models of eclipsing variable light curves were then tested on several real systems. For XY Bootis, we also compare in details the results obtained using our phenomenological modelling with those found using available physical models. We demonstrate that the proposed phenomenological models of transiting exoplanet and eclipsing binary light curves applied to ground-based photometric observations yields results compatible with those obtained by the application of more complex physical models. The suggested phenomenological modelling appears useful to solve a number of common tasks in the field of eclipsing variable research.Comment: 13 pages, 14 figures. To appear in Astronomy and Astrophysics, 201

Segmentwise Discrete Wavelet Transform

Dizertační práce se zabývá algoritmy SegDWT pro segmentový výpočet Diskrétní Waveletové Transformace – DWT jedno i vícedimenzionálních dat. Segmentovým výpočtem se rozumí způsob výpočtu waveletové analýzy a syntézy po nezávislých segmentech (blocích) s určitým překryvem tak, že nevznikají blokové artefakty. Analyzující část algoritmu pracuje na principu odstranění přesahu a produkuje vždy část waveletových koeficientů z waveletové transformace celého signálu, které mohou být následně libovolně zpracovány a podrobeny zpětné transformaci. Rekonstruované segmenty jsou pak skládány podle principu přičtení přesahu. Algoritmus SegDWT, ze kterého tato práce vychází, není v současné podobně přímo použitelný pro vícerozměrné signály. Tato práce obsahuje několik jeho modifikací a následné zobecnění pro vícerozměrné signály pomocí principu separability. Kromě toho je v práci představen algoritmus SegLWT, který myšlenku SegDWT přenáší na výpočet waveletové transformace pomocí nekauzálních struktur filtrů typu lifting.The dissertation deals with SegDWT algorithms performing a segmented (segmentwise) computation of one- and multi-dimensional Discrete Wavelet Transform – DWT. The segmented approach allows one to perform the segment (block) wavelet analysis and synthesis using segment overlaps while preventing blocking artifacts. The parts of the wavelet coefficients of the whole signal wavelet transform corresponding to the actual segment are produced by the analysis part of the algorithm exploiting overlap-save principle. The resulting coefficients belonging to the segment can be processed arbitrarily and than they can transformed back to the original domain. The reconstructed segments are than put together using overlap add principle. The already known SegDWT algorithm can not be effectively used on multidimensional signals. Several modifications of the algorithm are proposed which makes it possible to generalize it to multidimensional cases using separability property. In addition, the thesis presents SegLWT algorithm adopting ideas of the SegDWT and transferring it to the non-causal lifting filter bank structures.