Descripción: In this paper we compare two methods, based on the Gabor and wavelet transforms, to quantify and visualize the time evolution of frequency contents of electroencephalogram (EEG) time series. We found an optimal correlation between EEG visual inspection and the proposed methods in the characterization of the frequency and energy content of characteristic activity during an epileptic seizure. The quasimonofrequency behavior observed in the epileptic EEG series, in a previous work using a Gabor analysis [J. Inst. Electr. Eng. 93, 429 (1946)], is confirmed with the analysis using a wavelet. Moreover, the method based on the wavelet transform allows us to build a detector of epileptic events. Both methods are exemplified with EEG series obtained with depth electrodes in refractory epileptic patients. © 1996 The American Physical Society.

Descripción: A procedure for the construction of balanced orthogonal nonseparable quincunx multiwavelets, having filters with good lowpass properties, is introduced. The matrix filter bank is viewed as the polyphase matrix of other filters, upon which the lowpass condition is imposed. The multiscaling functions obtained are plotted by means of the cascade algorithm. The process of transforming an image with these wavelets is outlined: formulae for analysis and synthesis are given, the first steps are illustrated with images, and the decomposition of the original image into two input images is addressed. Compression is achieved in a nonlinear process. Experimental results show that (i) the constructed multiwavelets having lowpass properties perform better than other nonseparable multiwavelets, (ii) the energy compaction in the fine detail subbands is greater for the multiwavelets than for the one-dimensional wavelets tried.

Descripción: Above the southern Andes range and its prolongation in the Antarctic Peninsula, large-amplitude mountain and shear gravity waves observed with Weather Research and Forecasting (WRF) mesoscale model simulations during winter 2009 are analyzed. Two specific reasons motivated this study: (1) a decade of satellite observations of temperature fluctuations in the stratosphere, allowing us to infer that this region may be launching the largest-amplitude gravity waves into the upper atmosphere, and (2) the recent design of a research program to investigate these features in detail, the Southern Andes Antarctic Gravity wave Initiative (SAANGRIA). The simulations are forced with ERA-Interim data from the European Centre for Medium-Range Weather Forecasts. The approach selected for the regional downscaling is based on consecutive integrations with weekly reinitialization with 24 h of spin-up, and the outputs during this period are excluded from the analysis. From 1 June to 31 August 2009, five case studies were selected on the basis of their outstanding characteristics and large wave amplitudes. In general, one or two prevailing modes of oscillation are identified after applying continuous wavelet transforms at constant pressure levels and perpendicularly to the nominal orientation of the dominant wave crests. In all cases, the dominant modes are characterized by horizontal wavelengths around 50 km. Their vertical wavelengths, depending on a usually strong background wind shear, are estimated to be between 2 and 11 km. The corresponding intrinsic periods range between 10 and 140 min. In general, the estimated vertical wavelength (intrinsic period) maximizes (minimizes) around 250-300 hPa. The synoptic circulation for each case is described. Zonal and meridional components of the vertical flux of horizontal momentum are shown in detail for each case, including possible horizontal wavelengths between 12 and 400 km. Large values of this flux are observed at higher pressure levels, decreasing with increasing height after a progressive deposition of momentum by different mechanisms. As expected, in the wintertime upper troposphere and lower stratosphere in this region, a prevailing zonal component is negative almost everywhere, with the exception of one case above the northern tip of the Antarctic Peninsula. A comparison with previous experimental results reported in the region from in situ and remote sensing measurements suggests a good agreement with the momentum flux profiles computed from the simulations. Partial wave reflection near the tropopause was found, as considerable departures from equipartition between potential and kinetic wave energy are obtained in all cases and at all pressure levels. This ratio was always less than 1 below the lower stratosphere. Copyright 2012 by the American Geophysical Union.