Wavelets

The increasing demand of World Wide Web raises the need of predicting the user's web page request. The most widely used approach to predict the web pages is the pattern discovery process of Web usage mining. This process involves inevitability of many techniques like Markov model, association rules and clustering. Fuzzy theory with different techniques has been introduced for the better results. Our focus is on Markov models. This paper is introducing the vague Rules with Markov models for more accuracy using the vague set theory.

Abstrak Kemampuan manusia untuk membedakan tekstur-tekstur yang berbeda secara perceptual merupakan permasalahan utama dalam visi mesin (machine vision) yang mengacu pada banyak pola tekstural dan kondisi iluminasi. Sehingga dalam beberapa dekade ini banyak dikembangkan penelitian teknik multiskala (multiscale) yang dapat mengisolasi daerah (region) yang mempunyai tekstur homogen secara perceptual dalam sebuah citra. Dari beberapa penelitian kebanyakan menggunakan citra gray-level yang mengabaikan unsur warna dari citra.Penelitian ini melakukan segmentasi citra berwarna berdasarkan karakteristik color-texture dengan menggunakan teknik multiskala, yaitu dengan menerapkan transformasi wavelet diskrit (Discrete Wavelet Transform) untuk mendapatkan region-region yang mempunyai tekstur yang homogen. Dalam metode ini, suatu citra disegmentasi dalam beberapa region dengan mengelompokkan (clustering) fitur color-texture yang diperhitungkan dari koefisien waveletnya. Percobaan dilakukan dengan menggunakan citra tekstur gray-level dan berwarna, serta citra riil. Dari hasil percobaan yang dilakukan, dapat dilihat bahwa hasil segmentasi region pada citra yang berwarna lebih dapat membedakan dua region yang mempunyai tekstur sama tetapi mempunyai warna yang agak berbeda. Pemilihan transformasi ruang warna juga mempengaruhi hasil segmentasi, dimana dari beberapa percobaan yang dilakukan transformasi ruang warna linier K-L (Karhunen-Loeve) memberikan hasil yang lebih baik dibandingkan transformasi ruang warna nonlinier HSV (Hue Saturation Value)

In order to measure the D structure of a number of objects a comparably new technique in computer vision exists, namely time of flight (TOF) cameras. The overall principle is rather easy and has been applied using sound or light for a long time in all kind of sonar and lidar systems. However in this approach one uses modulated light waves and receives the signals by a parallel pixel array structure. Out of the travelling time at each pixel one can estimate the depth structure of a distant object. The technique requires measuring the intensity differences and ratios of several pictures with extremely high accuracy; therefore one faces in practice rather high noise levels. Object features as reflectance and roughness influence the measurement results. This leads to partly high noise levels with variances dependent on the illumination and material parameters. It can be shown that a reciprocal relation between the variance of the phase and the squared amplitude of the signals exists. On...

Power Quality is the Major Concern in modern Electrical Distribution System. Supplying Un Interrupted Power to the customers is the first priority of distribution companies. In recent days, raise of un balanced loads the voltage levels are deviated, further causing many power quality issues. There is a constant need of monitoring the voltage, current levels of the distribution system. To achieve this, these parameters like voltage, current and power are continuously measured. Decomposed Signals are more effective than the Original Signals to analysis the Signal for detecting Power Quality disturbances. So, Signal Processing techniques are affective techniques to measure the voltage, current and Power. In this Paper, dual tree complex wavelets transform (DTCWT) is used to decompose the signal. A formula is proposed measure the power in distribution system using dual tree complex wavelet transform. The Proposed formula Validated by taking different cases and it is carried out in MATLAB Software.

Given the central role which demand plays in the cost of health care Money Matters has recently been exploring the issues around forecasting demand.  Having been involved in health care planning for over 18 years I have serious reservations about the central assumption in NHS planning that demographic change or the ageing population is driving demand.. In this respect increases in accident & emergency (A&E) attendances which are far above that suggested by demography are a common international feature. Fig. 1 elegantly demonstrates the complete lack of demographic involvement in that the A&E trends for England over the past 30 years behave in a way which has more to do with wavelet analysis, i.e. recurring peaks and troughs, rather than any other form of recognisable trend.

Head injury is a major reason for morbidity and mortality worldwide and traumatic head injuries represent the major cause of neurological disability to a clot or hematoma caused by Haemorrhage (ICH) and is the The most common cause of ICH normally reported in our country are road traffic accidents (RTA) followed by falls and assaults. India is a populous country with over a billion every 100,000 population with deprived of these doctors. The unavailability of these specialists is a grave concern to the w care to the nation. The mainstay in the diagnosis of an ICH is the CT (Computed Tomography) scan of the head which is the definitive tool for accurate diagnosis of an ICH following trauma and provides an objective assessment of structural damage to brain. Accurate segmentation of the haemorrhage. This study is on segment Keywords: Intracranial decomposition; Brain haemorrhage segmentation is the first step before detecting the been done on the brain haemorrhage detection using methods like Convolutional neural network other efficient and advanced deep learning techniques. But that is resource intensive. It is also nec efficient when there is a large dataset Hssayeni and colleagues multiple slices and made it public. Second, used deep learning methods to perform segmentation and got a dice coefficient of 31% which is good compared to and colleagues [12] propose entropy based automatic unsupervised brain intracranial haemorrhage segmentation which comprises of FCM clustering, thresholding and edge based active contour methods and they get a better result with the combination than FCM clustering and active use deep learning to diagnose brain haemorrhage. They have used LeNet, GoogleNet and Inception dataset consisting of 100 cases collected from 115 hospitals and discovered LeNet is the among the three. Arjun Majumdar and colleagues haemorrhage instead of Head injury is a major reason for morbidity and mortality worldwide and traumatic head injuries represent the major cause of neurological disability. A traumatic brain injury to a clot or hematoma caused by an accident or any other trauma. (ICH) and is the most common and serious consequence of head injury which can be life The most common cause of ICH normally reported in our country are road traffic accidents (RTA) followed by falls and assaults. India is a populous country with over a billion every 100,000 population with most of them in the urban setup, Indian rural population of more than 70% is deprived of these doctors. The unavailability of these specialists is a grave concern to the w care to the nation. The mainstay in the diagnosis of an ICH is the CT (Computed Tomography) scan of the head which is the definitive tool for accurate diagnosis of an ICH following trauma and provides an objective assessment of ctural damage to brain. Accurate segmentation of the. This study is on segmentation of the brain haemorrhage Intracranial haemorrhage; Discrete wavelet transforms I. RELATED WORK Brain haemorrhage segmentation is the first step before detecting the been done on the brain haemorrhage detection using methods like Convolutional neural network other efficient and advanced deep learning techniques. But that is resource intensive. It is also nec efficient when there is a large dataset, which is not easily available in case of brain haemorrhage. Hssayeni and colleagues [1][2] have contributed in two ways, they collected a new dataset of 82 CT scans with ade it public. Second, used deep learning methods to perform segmentation and got a dice coefficient of 31% which is good compared to other deep learning techniques on small datasets. Indrajeet Kumar propose entropy based automatic unsupervised brain intracranial haemorrhage segmentation which comprises of FCM clustering, thresholding and edge based active contour methods and they get a better result with the combination than FCM clustering and active contour methods alone. use deep learning to diagnose brain haemorrhage. They have used LeNet, GoogleNet and Inception dataset consisting of 100 cases collected from 115 hospitals and discovered LeNet is the among the three. Arjun Majumdar and colleagues [8] haemorrhage instead of traditional methods and achieve a Head injury is a major reason for morbidity and mortality worldwide and traumatic head injuries traumatic brain injury (TBI) is damage to the brain, secondary an accident or any other trauma. This hematoma is known as an Intracranial most common and serious consequence of head injury which can be life The most common cause of ICH normally reported in our country are road traffic accidents (RTA) followed by falls and assaults. India is a populous country with over a billion people and there is approximately one radiologist for of them in the urban setup, Indian rural population of more than 70% is deprived of these doctors. The unavailability of these specialists is a grave concern to the w care to the nation. The mainstay in the diagnosis of an ICH is the CT (Computed Tomography) scan of the head which is the definitive tool for accurate diagnosis of an ICH following trauma and provides an objective assessment of ctural damage to brain. Accurate segmentation of the haemorrhage is the first step before detecting the brain haemorrhage images using discrete wavelet transforms. iscrete wavelet transforms; Segmentation; RELATED WORK Brain haemorrhage segmentation is the first step before detecting the haemorrhage in the brain. A lot of work has been done on the brain haemorrhage detection using methods like Convolutional neural network other efficient and advanced deep learning techniques. But that is resource intensive. It is also nec which is not easily available in case of brain haemorrhage. have contributed in two ways, they collected a new dataset of 82 CT scans with ade it public. Second, used deep learning methods to perform segmentation and got a dice deep learning techniques on small datasets. Indrajeet Kumar propose entropy based automatic unsupervised brain intracranial haemorrhage segmentation which comprises of FCM clustering, thresholding and edge based active contour methods and they get a better result contour methods alone. Tong Duc Phong and colleagues use deep learning to diagnose brain haemorrhage. They have used LeNet, GoogleNet and Inception dataset consisting of 100 cases collected from 115 hospitals and discovered LeNet is the most time [8] use a modified version of U-Net to detect the brain traditional methods and achieve an overall specificity of 98.6% on the small dataset. Brain Haemorrhage Segmentation using Dircrete Wavelet Transform. the terms of the Creative Commons Attribution License; Which Permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source Head injury is a major reason for morbidity and mortality worldwide and traumatic head injuries (TBI) is damage to the brain, secondary This hematoma is known as an Intracranial most common and serious consequence of head injury which can be life-threatening. The most common cause of ICH normally reported in our country are road traffic accidents (RTA) followed by falls people and there is approximately one radiologist for of them in the urban setup, Indian rural population of more than 70% is deprived of these doctors. The unavailability of these specialists is a grave concern to the well-being of the health care to the nation. The mainstay in the diagnosis of an ICH is the CT (Computed Tomography) scan of the head which is the definitive tool for accurate diagnosis of an ICH following trauma and provides an objective assessment of is the first step before detecting the brain images using discrete wavelet transforms. Thresholding; Wavelet haemorrhage in the brain. A lot of work has been done on the brain haemorrhage detection using methods like Convolutional neural network [2][3][5][11] and other efficient and advanced deep learning techniques. But that is resource intensive. It is also necessary and which is not easily available in case of brain haemorrhage. Murtada D. have contributed in two ways, they collected a new dataset of 82 CT scans with ade it public. Second, used deep learning methods to perform segmentation and got a dice deep learning techniques on small datasets. Indrajeet Kumar propose entropy based automatic unsupervised brain intracranial haemorrhage segmentation which comprises of FCM clustering, thresholding and edge based active contour methods and they get a better result Tong Duc Phong and colleagues [13] use deep learning to diagnose brain haemorrhage. They have used LeNet, GoogleNet and Inception-ResNet and a most time-consuming model Net to detect the brain overall specificity of 98.6% on the small dataset.

An important obstacle in the life expectancy of high voltage equipment is the progressive and systematic damage to insulation systems caused by Partial Discharge (PD). The evolution of PD activity is symptomatic of the insulation state. The characterization of these PD patterns may provide additional information into the nature and extent of various defects. By looking at a new generation of recently developed piezoelectric sensors with notable features (economic, large broadband frequency response, flexible, miniature, etc.), this study will investigate the applicability of this technology as an efficient partial discharge detector. We will provide experimental validation through a comparative study using conventional system measurements which are widely recognized within the industry.

ABSTRACT :
The flood is the major phenomenon of the central delta of Niger. This flood spreads of the complex manner in the delta. Hydrological processes of flooding and drainage of the plains of the central delta are still badly known. In our study, we tried to develop a new and original method of the processing and the interpretation of the NOAA AVHRR remote sensing images. The objectives are mainly to study spatial and temporal variability of the flood, to map and to quantify flooded and covered surfaces and to detect the functional channels. The Methodology is based on the multi-temporal analyse of NOAA AVHRR pixels by using a tool based on wavelets transform. A preliminary tiresome work of geographic positioning, navigation and atmospheric corrections was undertaken.
The obtained results highlight the power of this tool. Indeed, the objectives were practically realized. The complexity of spatial and temporal evolution of flooded and covered surfaces has been showed. Thus, It seems possible to us to exploit the potentialities of NOAA satellites to realise similar objectives. Procedures of automation of the processing of the image data base were developed for this study.

RÉSUMÉ :

L’inondation est le phénomène majeur du delta central du Niger. Cette inondation se répand d’une manière complexe dans le delta. Les modalités de mise en eau et de vidange des plaines du delta central sont encore très mal connues. Dans notre étude, nous avons essayé de mettre au point une méthode nouvelle et originale de traitements et d’interprétations des images satellitales, provenant des satellites NOAA. Les objectifs sont principalement d’étudier les variations spatio-temporelles de l’inondation, de cartographier et de quantifier les surfaces inondées et végétalisées et de détecter les défluents fonctionnels. La méthodologie est fondée sur l’analyse multi-temporelle des pixels NOAA AVHRR en utilisant l’outil de la transformée en ondelettes. Un travail fastidieux préalable de recalage, de navigation et de corrections atmosphériques a été entrepris. Les résultats obtenus mettent en évidence la puissance de cet outil. En effet, les objectifs ont été globalement atteints. La complexité de l’évolution spatio-temporelle des surfaces inondées et végétalisées a été mise en évidence. Ainsi, Il nous semble possible d’exploiter les potentialités offertes par les satellites NOAA AVHRR pour répondre à des objectifs similaires. Des procédures d’automatisation des traitements d’une base de données de type image ont été développées pour cette étude.

La clasificación automática de las imágenes del Diagnóstico de Esparcimiento Thomson constituye uno de los ejes de la automatización del funcionamiento del TJ – II. En consecuencia el sistema de adquisición de datos del Diagnóstico fue sincronizado con el funcionamiento del TJ – II y un clasificador automático de imágenes desarrollado, funcionando este hace algunos años. Este trabajo se centra en el diseño y entrenamiento de nuevos clasificadores para las
imágenes del Diagnóstico de Esparcimiento Thomson. En el mismo se presenta un conjunto de clasificadores desarrollados para la clasificación de las imágenes del Diagnóstico. Los referidos clasificadores fueron diseñados para el funcionamiento en dos etapas, una de preprocesamiento de las imágenes, en la cual se utilizan las
transformadas wavelet, y otra de clasificación, en la cual se recurre a distintas técnicas de aprendizaje, las redes neuronales Learning Vector Quantization, las Máquinas de Vectores Soporte y template matching. Se presenta también una serie de experimentos realizados con los referidos clasificadores y con base en los resultados obtenidos se efectúa un análisis comparativo en cuanto a las potencialidades de los
mismos. Por otro lado, se presenta en el trabajo un servidor de clasificación desarrollado con base en uno de los clasificadores aquí presentados. El referido servidor se integra al sistema de adquisición de datos del Diagnóstico y permite efectuar la clasificación de las imágenes, a petición de un programa cliente, de forma sincronizada con el funcionamiento del TJ – II.
Palabras Claves: redes neuronales, Learning Vector Quantization, Máquina de Vectores Soporte, template matching, clasificador
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Automatic classification of Thomson Scattering Diagnostic’s images is among the central ideas about the TJ – II automation. Consequently, the Diagnostic’s data acquisition program has been synchronized with the TJ – II operation and an automatic image classifier implemented, and it has been operating for years. This work aims to design and train a set of new classifiers for the Thomson Scattering Diagnostic’s images. In this work a set of classifiers developed for the Diagnostic’s images are shown. They were designed to operate in two stages, firstly the preprocessing stage, in which the wavelet transform is used, and then the classification
stage, in which several learning techniques are used, as Learning Vector Quantization neural networks, Support Vector Machines and template matching. Also, a set of experiments carried out with the designed classifiers are shown and based on the tests performances a comparative analysis is made. On the other hand, in the work a classification server, which were developed using one of the showed classifiers, is presented. The server is integrated in the Diagnostic’s data
acquisition system and allows image classification, at request of a client program, in a synchronized way with TJ – II operation.
Keywords: neural networks, Learning Vector Quantization, Support vector Machines, template matching, classifier

Soft computing is likely to play an important role in science and engineering in the future. The successful applications of soft computing and the rapid growth suggest that the impact of soft computing will be felt increasingly in coming years. Soft Computing encourages the integration of soft computing techniques and tools into both everyday and advanced applications. This Open access peer-reviewed journal serves as a platform that fosters new applications for all scientists and engineers engaged in research and development in this fast growing field.

Image processing and analysis based on the continuous or discrete image transforms are classic techniques. The image transforms are widely used in image filtering, data description, etc. Nowadays the wavelet theorems make up very popular methods of image processing, denoising and compression. Considering that the Haar functions are the simplest wavelets, these forms are used in many methods of discrete image transforms and processing. The image transform theory is a well known area characterized by a precise mathematical background, but in many cases some transforms have particular properties which are not still investigated. This paper for the first time presents graphic dependences between parts of Haar and wavelets spectra. It also presents a method of image analysis by means of the wavelets-Haar spectrum. Some properties of the Haar and wavelets spectrum were investigated. The extraction of image features immediately from spectral coefficients distribution were shown. In this pa...

A compressão de dados é um dos factores que mais contribuiu para o grande crescimento das tecnologias da informação e da comunicação. Sem compressão, a maioria dos produtos tecnológicos de consumo e entretenimento, que são hoje banais, nunca teria chegado a existir, destacando-se, entre muitos outros, o DVD, as câmaras fotográficas digitais, os leitores de MP3, o YouTube e o streaming de vídeo, as redes sem fios e a televisão digital. De facto, as tecnologias de compressão multimédia permitem representar a informação de uma forma mais eficiente, reduzindo os grandes volumes de espaço de armazenamento que ocupa e, portanto, a largura de banda que consome para se transmitir nas redes e na Internet. Este livro tem como objectivo principal apresentar uma introdução fundamentada, clara, acessível e abrangente aos conceitos e tecnologias relacionadas com métodos, algoritmos e normas internacionais de compressão de informação multimédia. Ao longo do livro são abordados, entre outros, os seguintes temas: Conceitos e normas sobre compressão de informação multimédia, incluindo texto, imagens, áudio e vídeo; Entropia e algoritmos de compressão sem perdas: Shannon-Fano, Huffman, Aritmética e LZW; Psicoacústica, métodos e normas de compressão de áudio, incluindo voz (ADPCM, vocoders) e áudio de alta-fidelidade (transformadas, MP3, AAC, MP4 e Dolby AC-3); Teoria rate-distortion, métodos de compressão de imagem (DPCM, transformadas DCT, waveletet Haar, quantificadores lineares e não-lineares); Normas internacionais JPEG e JPEG2000; Compressão de vídeo, redundância espacial e temporal, quantificação de vídeo para aplicações multimédia e de videoconferência; Normas MPEG.

Decision making both on individual and organizational level is always accompanied by the search of other's opinion on the same. With tremendous establishment of opinion rich resources like, reviews, forum discussions, blogs, micro-blogs, Twitter etc provide a rich anthology of sentiments. This user generated content can serve as a benefaction to market if the semantic orientations are deliberated. Opinion mining and sentiment analysis are the formalization for studying and construing opinions and sentiments. The digital ecosystem has itself paved way for use of huge volume of opinionated data recorded. This paper is an attempt to review and evaluate the various techniques used for opinion and sentiment analysis.

With the computational power available today, machine learning is becoming a
very active field finding its applications in our everyday life. One of its biggest
challenge is the classification task involving data representation (the preprocess-
ing part in a machine learning algorithm). In fact, classify linearly separable
data is easily done. The aim of the preprocesing part is to obtain well repre-
sented data by mapping raw data into a feature space where simple classifiers
can be used efficiently. For example, everything around audio processing uses
MFCC until now. This toolbox gives the basic tools for audio representation
using the C++ programming language by providing an implementation of the
Scattering Network [4] which brings a new and powerful solution for these tasks.
The toolkit of reference in scattering analysis is the SCATNET from Mallat et al.
1
. This tool is an attempt to have some of the scatnet features more tractable
in large dataset. Furthermore, the use of this toolbox is not limited to ma-
chine learning preprocessing. It can also be used for more advanced biological
analysis such as animal communication behaviours analysis or any biological
study related to signal analysis. One motivation for this work is the collabora-
tion between DI ENS and the university of Toulon through the SABIOB Scaled
Acoustic project.[15] [14]. This toolbox gives out of the box executables that can
be used by simple bash commands. Examples are given in the README file.
Finally, for each presented algorithm, a graph is provided in order to summarize
how the computation is done in this toolbox.

The trend for coloring gray scale mages becomes very interesting research
point nowadays since it is utilized to increase the visual appeal of images such as old
black and white photos, movies or scientific illustrations, and different techniques for
doing that exist in the literature. There are many traditional ways for coloring like
hand-coloring and pseudocoloring, but the trend for automatic computer based
coloring is an important goal for many researchers in this field. From our side of view
all these trials are still depend on human interaction in the coloring process.
In this thesis, we propose a new system for automatic gray image coloring. The
proposed system is constructed of texture based recognition system that recognizes the
objects in textural images like natural scenes, and then retrieve their actual colors from
a previous knowledge about their classes. This procedure is a trial of simulating the
human vision in this area.
The proposed Texture Recognition based Image Coloring System (TRICKS) is
composite of three stages; segmentation stage to segment the image into different
regions according to their textural characteristics, classification stage to classify or
recognize each region to be one of a predefined set of texture classes. For each class, a
hue color is attached which is transferred to the regions of this class in the final stage,
the coloring stage.
This thesis is a research work for studying different gray image features, segmentation
and classification techniques, and different color modes to select the suitable
techniques for achieving the best coloring results.

In the present technical report the Discrete Wavelet Transform is introduced. The z- transform and the discrete Fourier transform along with their properties are first reviewed. Then the up-sampling and down-sampling processes are described. Subband transforms, two-channel analysis/synthesis filter banks and quadrature mirror filters follow. Finally, the discrete wavelet transform is introduced and its subband implementation is described.

The present contribution presents a review of the research on the use of wavelets as a medium of fault detection and fault tolerant control of induction machines. Modeling of induction motor in the stator short winding and stator open winding faults has been illustrated. The authors provide comprehensive information about the wavelet application to fault diagnosis, including a summary of wavelet types (continuous and discrete), faults, methods and their validation in the diagnosis and frequency characteristics components of healthy and faulty induction motors. Inverter faults and artificial intelligence methods used for fault diagnosis are reviewed in this paper. Case studies using stator current sensing, DC voltage sensor and the gate drive signal for fault detection of an induction motor are also presented. Finally, a case study of inverter fault detection is illustrated experimentally using an induction motor drive controlled by the Texas Instrument TMS 320F28335 DSP.

En este  trabajo, se desarrolló una interfaz  en MatLab preparada  para cuantificar de manera sistemática  el desempeño de  distintos algoritmos  para reconstruir imágenes médicas obtenidas por ultrasonido.  Los filtros  seleccionados  utilizan umbrales duros y blandos  aplicados a  los coeficientes wavelet de la imagen exportada del ecógrafo.  Las transformadas elegidas  son  transformadas discreta wavelet (DWT)  [26],  [59], transformadas Daubechies wavelets simétricas (SDW)  [54],  [55], onditas complejas de doble árbol (DT-CWT)  [47],  [66], phaselet  [28],  [29] y curvelet  [15][81]. Según el estado del arte actual, estas transformadas corresponden al conjunto de las que  obtienen mejores resultados de reducción de ruido tipo speckle. 
La plataforma integra distintas métricas objetivas que utilizan referencia externa (pico de relación señal ruido - PSNR), que utilizan referencia reducida (ganancia de contraste – CG) y que no necesitan referencia alguna (resolución lateral  - RL, resolución axial  - RA). Así mismo, la misma fue desarrollada para cuantificar estás métricas, no solo sobre la imagen total, sino también en entornos definidos por el usuario, variando posición y cantidad de pixeles. 
En este trabajo,  se propone un método  consistente  que  implica  obtener la imagen mediante la captura de un fantoma conocido (en este caso, un fantoma multipropósito comercial), con zonas de distintas impedancias y tamaños. De esta manera, generar la imagen utilizada como referencia a partir de las especificaciones técnicas brindadas por el fabricante.
Se realizaron pruebas  sobre  imágenes  obtenidas a partir de la captura  un fantoma Gammex 403 GS LE por un ecógrafo Esaote MyLabTM  25, aplicando umbrales duros y blandos a los coeficientes wavelet. Se compararon los distintos descriptores en entornos de objetivos infinitesimales y quistes de distinta impedancia. A partir de estas pruebas, se puede concluir que los valores de mejora sobre la PSNR no siempre reflejan una mejora en otros índices importantes.

Wavelets have been favorably applied in almost all aspects of digital wireless communication systems including data compression, source and channel coding, signal denoising, channel modeling and design of transceivers. The main property of wavelets in these applications is in their flexibility and ability to characterize signals accurately. In this paper recent trends and developments in the use of wavelets in wireless communications are reviewed. Major applications of wavelets in wireless channel modeling, interference mitigation, denoising, OFDM modulation, multiple access, Ultra Wideband communications, cognitive radio and wireless networks are surveyed. The confluence of information and communication technologies and the possibility of ubiquitous connectivity have posed a challenge to developing technologies and architectures capable of handling large volumes of data under severe resource constraints such as power and bandwidth. Wavelets are uniquely qualified to address this challenge. The flexibility and adaptation provided by wavelets have made wavelet technology a strong candidate for future wireless communication.

The paper proposes a new image encryption scheme based on chaotic encryption. It provides a fast encryption algorithm based on coupled chaotic map. The image is encrypted using a pseudorandom key stream generator. The image is partially encrypted by selecting most important components of image. To obtain most important components of an image, discrete wavelet transform is applied.

Uma sinopse sobre séries ortogonais generalizadas (e.g. Legendre-Fourier), com ênfase na representação trigonométrica de Fourier, é introduzida. A apresentação envolve o fenômeno de Gibbs, e critérios para a convergência de séries (condições de Dirichlet, teorema de Fourier, teorema de Fejér). Implicações do “Reino de Fourier” na Engenharia Acústica: consonâncias & dissonâncias, instrumentos musicais.  Apresenta-se a teoria dos tapers de Tukey, a janela de Lanczos e o uso da série de Fourier para modelar fractais determinísticos. A passagem para o contínuo conduz à transformada de Fourier, cujas propriedades são revisadas. O princípio da incerteza de Gabor-Heisenberg é conectado à teoria de Fourier. Cálculos computacionais do espectro conduzem à transformada discreta de Fourier (DFT) e mecanismos para o cálculo eficiente do espectro (algoritmos rápidos). Os resultados de Heidman sobre complexidade multiplicativa para a DFT são apresentados. A análise espectral clássica evolui: a análise moderna com base em wavelets funciona ligada à abordagem Fourier. O teorema da amostragem é discutido, com uma demonstração do tipo “viva Fourier”, assim como o teorema 2BT sobre dimensionalidade de sinais. Aplicações modernas na descontaminação de sinais são argumentadas sob enfoque pragmático. A adaptação da análise de Fourier para sinais estocásticos conduz às séries estocásticas de Fourier, e expansões de Kahunen-Loève. Até a modelagem não-linear para sistemas com base em séries de Volterra é apresentada. Por fim, o reino de Fourier conquista definitivamente o mundo finito e digital, migrando para a transformada de Fourier de corpo finito (transformada de Galois-Fourier).

Identifying spatio-temporal synchrony in a complex, interacting and oscillatory coupled-system is a challenge. In particular, the characterization of statistical relationships between environmental or biophysical variables with the multivariate data of pandemic is a difficult process because of the intrinsic variability and non-stationary nature of the time-series in space and time. This paper presents a methodology to address these issues by examining the bivariate relationship between Covid-19 and temperature time-series in the time-localized frequency domain by using Singular Value Decomposition (SVD) and continuous cross-wavelet analysis. First, the dominant spatio-temporal trends are derived by using the eigen decomposition of SVD. The Covid-19 incidence data and the temperature data of the corresponding period are transformed into significant eigen-state vectors for each spatial unit. The Morlet Wavelet transformation is performed to analyse and compare the frequency structure of the dominant trends derived by the SVD. The result provides cross-wavelet transform and wavelet coherence measures in the ranges of time period for the corresponding spatial units. Additionally, wavelet power spectrum and paired wavelet coherence statistics and phase difference are estimated. The result suggests statistically significant coherency at various frequencies providing insight into spatio-temporal dynamics. Moreover, it provides information about the complex conjugate dynamic relationships in terms phases and phase differences.

A methodological analyze of a time series issued from several space geodesy techniques (Doris stations position, mean sea level at global and local scales) is performed trough this thesis.
This study concerns, in the first step, an comparative analyze of the time series of position of six DORIS stations issued from three international analysis centers (Institute of Astronomy, Russian Academy of Sciences, Russia /INA, Institut Géographique National, IGN France; and CNES/ CLS Centre d’Analyse, France /LCA), using the wavelet spectral technique for the determination of the correlation between the different analysis centers. The obtained results confirm the strong correlation between the solutions of the two analysis centers IGN and INA.
To highlight the efficiency of the technique used, an application using data from satellite altimetry is steadily successfully performed for showing the strong correlation between the variations of the global mean sea level and the fluctuations of the ENSO (El Niño Southern Oscillation) phenomena as well as their relative phases in the time – frequency space.
As a similar technique to the wavelet analysis, the SSA (Singular Spectrum Analysis) is applied for the time series of the mean sea and ocean levels. The trends extracted well confirm the rise of the mean sea and oceans levels, and therefore these trends highlight the strong regional signature.
Key words: Time series, Position of stations, sea level, wavelet, correlation, SSA.