Zolotarev polynomials utilization in spectral analysis

Tato práce je zaměřena na vybrané problémy Zolotarevových polynomů a jejich vyuľití ke spektrální analýze. Pokud jde o Zolotarevovy polynomy, jsou popsány základní vlastnosti symetrických Zolotarevových polynomů včetně ortogonality. Rovněľ se provádí prozkoumání numerických vlastností algoritmů generujících dokonce Zolotarevovy polynomy. Pokud jde o aplikaci Zolotarevových polynomů na spektrální analýzu, je implementována aproximovaná diskrétní Zolotarevova transformace, která umoľňuje výpočet spektrogramu (zologramu) v reálném čase. Aproximovaná diskrétní zolotarevská transformace je navíc upravena tak, aby lépe fungovala při analýze tlumených exponenciálních signálů. A nakonec je navrľena nová diskrétní Zolotarevova transformace implementovaná plně v časové oblasti. Tato transformace také ukazuje, ľe některé rysy pozorované u aproximované diskrétní Zolotarevovy transformace jsou důsledkem pouľití Zolotarevových polynomů.This thesis is focused on selected problems of symmetrical Zolotarev polynomials and their use in spectral analysis. Basic properties of symmetrical Zolotarev polynomials including orthogonality are described. Also, the exploration of numerical properties of algorithms generating even Zolotarev polynomials is performed. As regards to the application of Zolotarev polynomials to spectral analysis the Approximated Discrete Zolotarev Transform is implemented so that it enables computing of zologram in real–time. Moreover, the Approximated Discrete Zolotarev Transform is modified to perform better in the analysis of damped exponential signals. And finally, a novel Discrete Zolotarev Transform implemented fully in the time domain is suggested. This transform also shows that some features observed using the Approximated Discrete Zolotarev Transform are a consequence of using Zolotarev polynomials

Discrepancies in perception and evaluation of macroenvironment – sectoral analysis

The aim of presented study is to evaluate macroeconomic environment and to determine differences in perception of macroeconomic environment by entrepreneurs in Slovak Republic and Czech Republic. Data collection was done by questionnaire which was answered by 329 entrepreneurs from Slovak Republic and 312 entrepreneurs from Czech Republic. Topics treated concerning macroenvironment were the favourableness of macroenvironment for business activities, its support for starting an entrepreneurship, its support of innovation activities of companies and its capacity to promote entrepreneurship and to create interesting business opportunities. Answers are divided according to sector in which entrepreneurs doing business. Considered sectors are: transport, trade, construction, production, agriculture, services and other sectors. To analyse collected data, we use correspondence analysis. Results show that there exists systematic difference in perception of macroenvironment by entrepreneurs from SMEs in Slovak Republic and Czech Republic. It seems that entrepreneurs from Czech Republic percept macroenvironment more positively than Slovak ones. Moreover, we document different perception of macroeconomic situation depending on sector in which entrepreneurs operate. Presented research results bring findings for the creators of economic policies. Similarly, presented results form a platform for concepts of strategic and regional plans in order to provide sustainable business environment in the countries, and also their stable economic growth.Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic; Slovak Academy Sciences [VEGA 1/0797/20

Hardware accelerator for a selective transforms

katedra elektromagnetického pol

A Novel Spectral Zoom Method based on Zolotarev Polynomials

This paper discusses the usage of symmet rical Zolotarev polynomials (ZPS)s in spectral analysis. Evaluation of Discrete Zolotarev transform (DZT) coeffi cients is briefly discussed. However, the DZT coefficients evaluation is problematic. An alternative novel method embedding ZPSs is proposed. The novel method, so-called DZT zoom, improves the spectrum’s time resolution for non-stationary signals compared to narrowband spectro gram. Results are comparable to the approximated DZT (ADZT). The DZT zoom distinguishing property is the focus on a particular frequency band of the spectrum