Since 2000, the southwestern Brazilian Amazon has undergone a rapid transformation from natural vegetation and pastures to row-crop agricultural with the potential to affect regional biogeochemistry. The goals of this research are to assess wavelet algorithms applied to MODIS time series to determine expansion of row-crops and intensification of the number of crops grown. MODIS provides data from February 2000 to present, a period of agricultural expansion and intensification in the southwestern Brazilian Amazon. We have selected a study area near Comodoro, Mato Grosso because of the rapid growth of row-crop agriculture and availability of ground truth data of agricultural land-use history. We used a 90% power wavelet transform to create a wavelet-smoothed time series for five years of MODIS EVI data. From this wavelet-smoothed time series we determine characteristic phenology of single and double crops. We estimate that over 3200 km(2) were converted from native vegetation and pasture to row-crop agriculture from 2000 to 2005 in our study area encompassing 40,000 km(2). We observe an increase of 2000 km(2) of agricultural intensification, where areas of single crops were converted to double crops during the study period. (C) 2007 Elsevier Inc. All rights reserved.

We use wavelet analysis to study cycle synchronization across the EU-15 and the Euro-12 countries. Based on the wavelet transform, we propose a metric to measure and test for business cycles synchronization. Several conclusions emerge. France and Germany form the core of the Euro land, being the most synchronized countries with the rest of Europe. Portugal, Greece, Ireland and Finland do not show statistically relevant degrees of synchronization with Europe. We also show that some countries (like Spain) have a French accent, while others have a German accent (e.g. Austria). Perhaps surprisingly, we find that the French business cycle has been leading the German business cycle as well as the rest of Europe. Among the countries that may, in the future, join the Euro, the Czech Republic seems the most promising candidate.; Fundação para a Ciência e a Tecnologia (FCT) - PTDC/ECO/64750/2006

We use wavelet analysis to study business cycle synchronization across the EU-15 and the Euro-12 countries. Based on the wavelet transform, we propose a metric to measure and test for business cycles synchronization. Several conclusions emerge. France and Germany form the core of the Euro land, being the most synchronized countries with the rest of Europe. Portugal, Greece, Ireland and Finland do not show statistically relevant degrees of synchronization with Europe. We also show that some countries (like Spain) have a French accent, while others have a German accent (e.g., Austria). Perhaps surprisingly, we find that the French business cycle has been leading the German business cycle as well as the rest of Europe. Among the countries that may, in the future, join the Euro, the Czech Republic seems the most promising candidate.; Fundação para a Ciência e a Tecnologia (FCT)

We characterize the interrelation of CO2 prices with energy prices (gas and electricity), and with economic activity. Previous studies have relied on time-domain techniques, such as Vector Auto-Regressions. In this study, we use multivariate wavelet analysis, which operates in the time-frequency domain. Wavelet analysis provides convenient tools to distinguish relations at particular frequencies and at particular time horizons. Our empirical approach has the potential to identify relations getting stronger and then disappearing over specific time intervals and frequencies. We are able to examine the coherency of these variables and lead-lag relations at different frequencies for the time periods in focus.; COMPETE, QREN, FEDER, Fundação para a Ciência e a Tecnologia (FCT)

In 2008, a radio receiver that works in very low frequency (VLF; 20-60 kHz) and LF (150-300 kHz) bands was developed by an Italian factory. The receiver can monitor 10 frequencies distributed in these bands, with the measurement for each of them of the electric field intensity. Since 2009, to date, six of these radio receivers have been installed throughout Europe to establish a ‘European VLF/LF Network’. At present, two of these are into operation in Italy, and the remaining four are located in Greece, Turkey, Portugal and Romania. For the present study, the LF radio data collected over about two years were analysed. At first, the day-time data and the night-time data were separated for each radio signal. Taking into account that the LF signals are characterized by ground-wave and sky-wave propagation modes, the day-time data are related to the ground wave and the night-time data to the sky wave. In this framework, the effects of solar activity and storm activity were defined in the different trends. Then, the earthquakes with M ≥5.0 that occurred over the same period were selected, as those located in a 300-km radius around each receiver/transmitter and within the 5th Fresnel zone related to each transmitter-receiver path. Where possible...

Since 2009 a network of VLF (20-60 kHz) and LF (150-300 kHz) radio receivers was put into operation in Europe in order to study the disturbances produced by the earthquakes on the propagation of these signals. In 2011 the network for LF signals was formed by six receivers located two in Italy and one in Greece, Portugal, Romania, and Turkey. The LF radio data collected during about two years have been analysed. Each radio signal has been split in day-time and night-time data; then, the earthquakes with M 5.0, occurred in the same period, located in a 300 km radius around each receiver/transmitter and within the 5th Fresnel zone related to each transmitter-receiver path, have been selected. In this study we adopt the Principal Component Analysis (PCA) to study the radio signal anomalies possibly related to earthquake activity. A detailed comparison with similar studies that use wavelet analysis is done and advantages or drawback of the two methods are pointed out.

Dissertação para obtenção do Grau de Doutor em Alterações Climáticas e Políticas de Desenvolvimento Sustentável; Carbon markets’ goal is to promote the reduction of emissions of greenhouse gases where it is most cost-efficient. This makes the price of the tradable good – carbon dioxide equivalent (CO2e) - a key variable in management and risk decisions, in markets related to activities connected with the burning of fossil fuels, such as power generation. This work aims to improve the analysis of carbon prices’ dynamics, considering the possibility of multidirectional effects between prices of CO2e, energy (primary and final), offsets licenses and the economy performance, in various frequencies. The two main research questions are: (i) what drives carbon price variations? (ii) what variations do carbon prices drive? We used two comple-mentary methodologies: (a) a vector autoregression model (of common use in macroeconomics and financial markets but not in carbon-energy relations), which allows the analysis of causality and of impulse-response functions of daily prices; and (b) an innovative multivariate wavelet analysis, which allows us to understand the relationship and causal link between the variables in the time and frequency dimensions...

Nowadays, wavelet analysis of turbulent flows have become increasingly popular. However, the study of geometric characteristics from wavelet functions is still poorly explored. In this work we compare the performance of two wavelet functions in extracting the coherent structures from solar wind velocity time series. The data series are from years 1996 to 2002 (except 1998 and 1999). The wavelet algorithm decomposes the annual time-series in two components: the coherent part and non-coherent one, using the daubechies-4 and haar wavelet function. The threshold assumed is based on a percentage of maximum variance found in each dyadic scale. After the extracting procedure, we applied the power spectral density on the original time series and coherent time series to obtain spectral indices. The results from spectral indices show higher values for the coherent part obtained by daubechies-4 than those obtained by the haar wavelet function. Using the kurtosis statistical parameter, on coherent and non-coherent time series, it was possible to conjecture that the differences found between two wavelet functions may be associated with their geometric forms.

Ziel der Studie war es, festzustellen, ob sich im Vasomotionsmuster der Hautdurchblutung im Bereich psoriatischer Läsionen Veränderungen im Vergleich zu klinisch gesunder Haut desselben Patienten aufzeigen lassen. Methode: Bei 40 Patienten (13 Frauen und 27 Männer) mit Psoriasis vulgaris wurden simultan im Bereich klinisch gesunder Haut, sowie am Rand und in der Mitte einer psoriatischen Plaque mittels Laser- Doppler- Fluxmetrie (LDF) in liegender Körperposition kontinuierliche Messreihen der Hautdurchblutung mittels PC über einen Zeitraum von 10min und einer Abtastrate (fsamp) von 50Hz gespeichert. Diese so genannten LDF- Zeitreihen wurden bei einer Einzeldatenmenge von 2.048 Einzeldaten (entsprechend 40.96sec.), 4.096 Einzeldaten (entsprechend 81.92sec.) und 16.384 Einzeldaten (entsprechend 327.68sec.) mit modernen Analyseverfahren wie der Wavelet- Analyse oder der Biorthogonalzerlegung ausgewertet. Ergebnisse: In der linearen Analyse zeigt sich ein deutliches Überwiegen des mittleren LDF- Signals, unabhängig von der Länge der Datenreihe, in Bereichen psoriatischer Plaques (Mitte der Plaque > Rand der Plaque > gesunde Haut). In der Wavelet- Analyse zeigt sich ein Überwiegen der Herzaktion in psoriatischen Plaques gegenüber klinisch gesunder Haut (Mitte > Rand > gesunde Haut). Sowohl für den Einfluss der Atemaktivität als auch der Thermoregulation ist ein statistisch signifikant geringerer Anteil an der Vasomotion innerhalb der Plaque im Vergleich zu klinisch gesunder Haut nachweisbar (Mitte < Rand < gesunde Haut). Die innerhalb der Zeitreihe enthaltene Gesamtenergie (Etot) ist bei allen drei Einzeldatenmengen im Bereich der psoriatischen Plaque (Mitte > Rand) größer als in gesunder Haut. Hinsichtlich des Vasomotions- Skalierungs- Varianz- Kontrasts (VSV) zeigen sich für alle drei Datenlängen deutlich veränderte Flussmuster. Dabei weicht die Vasomotion in der Mitte der Läsion noch deutlicher von der Vasomotion im gesunden Hautareal ab...

Einleitung: Im Rahmen dieser Studie wurde mittels Laser Doppler Fluxmetrie (LDF) die Vasomotion im Basalzellkarzinom versus gesunde Haut analysiert und gemessen. Es sollte ermittelt werden, wie sich das Blutflussverhalten im Basalzellkarzinom versus gesunde Haut durch die Neoangiogenese verändert. Material und Methoden: Im Rahmen dieser Studie wurden 67 Patienten (davon 40 Männer/ 27 Frauen) mit einem histologisch gesicherten Basalzellkarzinom untersucht. Für die Messung kamen drei Laser Doppler Messsonden zum Einsatz. Die Messsonden wurden in der Mitte und im Randbereich des Basalzellkarzinoms und falls möglich kontralateral in einem von dem Basalzellkarzinom nicht betroffenen Hautgebiet befestigt. Simultan wurden Messwerte aus den drei Arealen erfasst und kontinuierlich mit dem PC gespeichert. Für das LDF wurden durch frühere Voruntersuchungen folgende unterschiedliche Skalierungsbereiche festgelegt: SL1: 0,026-0,056Hz Thermoregulation SL2: 0,056-0,16 Hz Eigenständige Gefäßwandregulation SL3: 0,16-0,56 Hz Atmungseinfluss SL4: 0,79-1,23 Hz Herzschlag Ergebnisse: Im Basalzellkarzinom war eine Abnahme des SL1 gegenüber der gesunden Haut zu registrieren. In allen anderen Skalierungsbereichen konnten wir statistisch signifikante Anstiege der einzelnen Skalierungsbereichen versus gesunde Haut zeigen. In der Tumormitte betrug der SL1 43...

Conference paper; Distributed wavelet processing within sensor networks holds promise for reducing communication energy and wireless bandwidth usage at sensor nodes. Local collaboration among nodes de-correlates measurements, yielding a sparser data set with significant values at far fewer nodes. Sparsity can then be leveraged for subsequent processing such as measurement compression, de-noising, and query routing. A number of factors complicate realizing such a transform in real-world deployments, including irregular spatial placement of nodes and a potentially prohibitive energy cost associated with calculating the transform in-network. In this paper, we address these concerns head-on; our contributions are fourfold. First, we propose a simple interpolatory wavelet transform for irregular sampling grids. Second, using ns-2 simulations of network traffic generated by the transform, we establish for a variety of network configurations break-even points in network size beyond which multiscale data processing provides energy savings. Distributed lossy compression of network measurements provides a representative application for this study. Third, we develop a new protocol for extracting approximations given only a vague notion of source statistics and analyze its energy savings over a more intuitive but naive approach. Finally...

Approved for public release; distribution is unlimited; Frequency hopped signals are widely used in various communication applications for their inherent security features. The demand, by civilian and governmental agencies, to intercept communication signals is increasing. The interception task can be summarized by detecting the signal's presence in additive noise, classifying the modulation type, estimating the control parameters, decoding the data, and decrypting the information content. This work addresses the merging of wavelet and correlation concepts to detect, classify and estimate the parameters of frequency hopped signals. We address the interception problem in two ways. The first approach is based on a visual inspection of the wavelet surfaces generated from the instantaneous correlation function of the communication signal and leads to hop start/stop times estimates. In the second approach, we apply an energy-based processing scheme to estimate the hop start and stop times, the hop scale pattern, and the hop frequency. Results show that frequency hopped signals can be identified at an SNR of 3 dB or 6 dB using visual inspection or an automated scheme, respectively; http://archive.org/details/waveletanalysiso00khal; Colonel...

Ultra-low-frequency (ULF) waves have been observed in the Mercury's magnetosphere. In this work, Mariner-10 and MESSENGER high resolution magnetic field data are studied with wavelet analysis. Two ULF wave intervals have been selected: 29 March 1974 (Mariner-10) and 14 January 2008 (MESSENGER). Non-stationary oscillations, with strong amplitude and narrow bandwidth have been found. The Mariner-10 ULF wave interval showed periods of ∼1.5-3.0 s, and the MESSENGER ULF wave interval had periods of ∼0.5-1.0 s. These periods of ULF waves are slightly longer than the proton gyroperiods (∼0.8 and ∼0.5 s, respectively). Therefore, these waves are most likely kinetic, not magnetohydrodynamic waves.

We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution scaling wavelet construction arise from a scale of Hilbert spaces. We study the theory of representations of the C*-algebra O_{\nu+1} arising from this multiresolution analysis.; Comment: 19 pages, REVTeX v. 3.1, submitted to J. Math. Phys., PACS 02.30.Nw, 02.30.Tb, 03.65.-w, 03.65.Bz, 03.65.Db. In the revision, the title is changed (from "Deformed multiresolution wavelet analysis of scale $\nu +1$"), some more introductory material is added, and some points both in the statements of results and their proof have been clarified

Using wavelet analysis approach, the temporal variations of solar activity on time scales ranging from days to decades, are examined from the daily time series of sunspot numbers. A hierarchy of changing complex periods are careful detected and related cycles compared with results from recent similar analyses. A general determination of the main Schwabe cycle length variations is also suggested on the basis of the wavelet amplitude distribution extracted from the local wavelet power map.; Comment: Postscript v1.1, 11 pages with 3 color figures

In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet functions and is named as the Fourier-Like and Hartley-Like wavelet analysis. A Hilbert transform analysis on the wavelet theory is also included.; Comment: 7 pages, 10 figures, Anais do XXII Simp\'osio Brasileiro de Telecomunica\c{c}\~oes, Campinas, 2005

This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of adeles $\bA$ by using infinite tensor products of Hilbert spaces. The adele ring is roughly speaking a subring of the direct product of all possible ($p$-adic and Archimedean) completions $\bQ_p$ of the field of rational numbers $\bQ$ with some conditions at infinity. Using our technique, we prove that $L^2(\bA)=\otimes_{e,p\in\{\infty,2,3,5,...}}L^2({\bQ}_{p})$ is the infinite tensor product of the spaces $L^2({\bQ}_{p})$ with a stabilization $e=(e_p)_p$, where $e_p(x)=\Omega(|x|_p)\in L^2({\bQ}_{p})$, and $\Omega$ is a characteristic function of the unit interval $[0,\,1]$, $\bQ_p$ is the field of $p$-adic numbers, $p=2,3,5,...$; $\bQ_\infty=\bR$. This description allows us to construct an infinite family of Haar wavelet bases on $L^2(\bA)$ which can be obtained by shifts and multi-delations. The adelic multiresolution analysis (MRA) in $L^2(\bA)$ is also constructed. In the framework of this MRA another infinite family of Haar wavelet bases is constructed. We introduce the adelic Lizorkin spaces of test functions and distributions and give the characterization of these spaces in terms of wavelet functions. One class of pseudo-differential operators (including the fractional operator) is studied on the Lizorkin spaces. A criterion for an adelic wavelet function to be an eigenfunction for a pseudo-differential operator is derived. We prove that any wavelet function is an eigenfunction of the fractional operator. These results allow one to create the necessary prerequisites for intensive using of adelic wavelet bases and pseudo-differential operators in applications.; Comment: 45 pages

A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be associated with a proper probability density, allowing defining the entropy of a wavelet. Introducing now the concept of wavelet mutual information between a signal and an analysing wavelet fulfils the foundations of a wavelet information theory (WIT). Both continuous and discrete time signals are considered. Finally, we showed how to compute the information provided by a multiresolution analysis by means of the inhomogeneous wavelet expansion. Highlighting ideas behind the WIT are presented.; Comment: 6 pages, 6 tables, VI International Telecommunications Symposium (ITS2006), September 3-6, Fortaleza, Brazil

Electrical signals generated by brain activity that are measured by the electroencephalogram can be distorted by electrical activity originating from eyeblinks and eye movements. This thesis proposes a new technique to identify and remove eyeblink artifacts from EEG data. An algorithm using a combination of wavelet analysis and independent component analysis (ICA) is implemented to detect the temporal location of the eyeblink artifact and eliminate it without compromising the integrity of the primary EEG data. The discrete wavelet transform is performed on 10 second epochs of data to detect the occurrence of ocular artifact. ICA is used to separate out the independent components within the data and the temporal locations of the eyeblink are used to remove the artifact and reconstruct the EEG data without that source of distortion. The results obtained indicate that the technique implemented may be robust enough to effectively process EEG data and is capable of removing eyeblink artifacts successfully when they are prominent and the data does not contain a great deal of movement artifact. The results show an 88.68% detection rate, a false positive rate of 4.03%, and an 87.23% removal rate for all eyeblinks that were accurately detected. The statistics obtained compared favorably with work done by others in this field of investigation.

We use a multiresolution analysis based on a wavelet transform to upscale two-dimensional heterogeneous permeability fields. Results are compared with conventional averaging upscaling schemes using arithmetic, geometric and harmonic averaging. It is found that the wavelet analysis is able to preserve the fine scale heterogeneous features with the increase of the coarse scale size significantly better than the averaging methods, while preserving information required for downsizing the properties of the system.