To improve the estimation of active power, the possibility of estimating the amplitude square of a signal component using the interpolation of the squared amplitude discrete Fourier transform (DFT) coefficients is presented. As with an energy-based approach, the amplitude square can be estimated with the squared amplitude DFT coefficients around the component peak and a suitable interpolation algorithm. The use of the Hann window, for which the frequency spectrum is well known, and the three largest local amplitude DFT coefficients gives lower systematic errors in squared interpolated approach or in better interpolated squared approach than the energy-based approach, although the frequency has to be estimated in the first step. All investigated algorithms have almost the same noise propagation and the standard deviations are about two times larger than the Cramér-Rao lower bound.
This study presents an attempt to design geographical visualisation tools that allow to tackle the immensity of spatial data provided by Volunteered Geographic Information (VGI), both in terms of temporal and spatial aspects. In accordance with the assumptions made at the conceptual stage, the final action was the implementation of the window entitled ‘Geovisualisation of the Panoramio.com Activities in District of Poznań 2011’ into the web browser. The concept has been based on a division of the geovisualisation window into three panels, of which the most important - in order to capture spatial variability - have statistical maps at the general level (dot map and choropleth map), while at the detailed level - a dot map on a topographic reference map or tourist map. For two ranges, temporal variability is presented by graphs, while a review of attributes of individual activities of the social website in question is set forward in the table panel. The element that visually interlinks all of the panels is the emphasised individual activity.
This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.