Fourier and Wavelet Processing

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.

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.

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).

The Colorado River flows more than 2400 kilometers, from its source in the Rocky Mountains in the United States through deserts and canyons, to the wetlands of a delta into the Gulf of California in Mexico. Detection of variations over the long term for a series of hydrological variables is an important and critical issue, which is subject to increasing interest because of the current topic of climate change. This study covers a 70 year time period from 1940 to 2010, using a Fast Fourier Transform (FFT) analysis of 118 daily precipitation sites located throughout the Colorado River basin. Tests for homogeneity and independence are applied to the data series; also a regression analysis is used just in specific cases. The data series of the stations is characterized as a function of frequency domain in order to identify a return rate of hydro-meteorological variables within the basin, verifying the existence of dominant periodic cycles in the data series. Different magnitudes in the precipitation periodicity are also examined. It is concluded that the precipitation of the Colorado River basin behaves in dominant periodic cycles of approximately 10.7 or 12.8 years. Nevertheless, there are three small areas in the basin which react in a different way: the mountains of Arizona showed a dominant period of 8 years; the higher elevations in the state of Colorado, 6.4 years; and the peaks of Wyoming, 4.6 years. These identified areas are the highest peaks where precipitation is more frequent. Besides, the moving average adjusts over a constant 13 year period for the data series of the stations. This suggests that precipitation in the basin completes a cycle every 13 years, verifying the FFT results. The FFT analysis may also be applied for frequency detection of other hydro-climatic variables such as temperature, humidity, streamflow and evapotranspiration.

In discussing the nature of the electromagnetic society and natural Law, Whitehead concludes by saying, “It is the ideal of mathematical physicists to formulate this systematic law in its complete generality for our epoch.” The Whiteheadian electromagnetic nexus in the human being merits further exploration and development in all dimensions, and may be modeled and explored by way of the modern mathematical transforms of information and communication theory.

Abstrak Penggunaan dekomposisi wavelet untuk pemodelan statistika khususnya pada data time telah mengala mi perkembangan yang pesat. Transformasi wavelet yang dipandang lebih sesuai untuk data time series adalah Maximal Overlap Discrete Wavelet Transform (MODWT) karena dalam setiap level dekomposisi terdapat koefisien wavelet dan skala sebanyak panjang data. Kelebihan ini mereduksi kelemahan pemfilteran dengan Discrete Wavelet Transform (DWT) yang tidak dapat dilakukan pada sebarang ukuran sampel. Penentuan level dekomposisi dan koefisien yang digunakan sebagai input model menggunakan dekomposisi multi skala. Dari analisis dapat disimpulkan data pasang surut Kota Semarang model yang terbaik digunakan adalah ARIMA ([3,12],1,0) karena mendapatkan nilai MSE minimal 40.90766. untuk permasalahan data surat keterangan asal (SKA) MSE minimal diperoleh pada dekomposisi level 1 dan banyaknya koefisien pada level tersebut adalah 3 dengan nilai MSE 150.4789. Kata Kunci: MODWT, time series 1. Pendahuluan Peramalan adalah suatu kegiatan memperkirakan apa yang terjadi pada masa yang akan datang berdasarkan nilai sekarang dan masa lalu dari suatu peubah (Makridakis, 1999). Peramalan merupakan suatu unsur yang sangat penting terutama dalam perencanaan dan pengambilan keputusan. Adanya tenggang waktu antara suatu peristiwa dengan peristiwa yang terjadi mendatang merupakan alasan utama bagi peramalan dan perencanaan. Dalam situasi tersebut peramalan merupakan alat yang penting dalam perencanaan yang efektif serta efisien.Pemilihan metode dalam peramalan tergantung pada beberapa aspek penilitian yaitu aspek waktu, pola data, tipe model sistem yang diamati, dan tingkat keakuratan peramalan. Penggunaan metode tersebut dalam peramalan harus memenuhi asumsi-asumsi yang digunakan. Analisis dekomposisi wavelet merupakan fungs i basis yang memberikan alat baru sebagai pendekatan yang dapat digunakan dalam merepresentasikan data atau fungsi-fungsi yang lain (Banakar dan Azeem, 2006). Algoritma wavelet mampu memproses data pada skala atau resolusi yang berbeda. Beberapa kajian yang berkaitan dengan transformasi wavelet telah banyak dibahas, diantaranya oleh Khashman dan Dimililer (2008) dan Mallat (1998). Beberapa kajian tentang transformasi wavelet pada data time series juga telah dilakukan, diantaranya oleh Murguia dan Canton (2006) serta Kozlowski (2005). Transformasi Wavelet akan menghasilkan himpunan koefisien Wavelet yang dihitung dari titik (lokasi) observasi pada level (skala) dan lebar range yang berbeda (Kozlowzki, 2005). Penghitunga n koefisien wavelet dapat dilakukan dengan Discrete Wavelet Transform (DWT) sebagaimana dikemukakan oleh Mallat (1998) atau Maximal Overlap Discrete Wavelet Transform (MODWT) seperti dalam Percival dan Walden (2000).

The efficient market hypothesis is one of most important theories in finance and one of the most important research areas for both developed and developing stock markets. In this study, the random-walk hypothesis is tested for the main stock markets of the G-20 countries. The linearity of the series is determined in the first stage. In this context, 16 of 17 markets have a linear structure; therefore, the Fourier ADF unit root test that uses trigonometric functions in order to capture deviations greater than the average of the dependent variable and takes into account multiple structural breaks, is applied to these series. Furthermore, the Fourier KSS unit root test that has the same functions as the Fourier ADF unit root test is used for the Japanese stock market, being the only one market with a non-linear structure. As the result of these analyses, while the markets of the nine countries are observed as effective in the weak form, this hypothesis is not valid for the remaining eight countries. While the prediction of the future price of all of these nine markets will be impossible through a technical analysis, investors in the remaining eight markets can provide returns by carrying out the same analysis.

Availability of rainfall time-series is limited in many parts of the World, and the continuity of such records is variable. This research endeavors to extend actual daily rainfall observations to ungauged areas, taking into account events of rainfall as well as cumulative total daily rainfall, over a period of 11 years. Results show that rainfall events histograms can be reconstructed, and that total cumulative rainfall is estimated with 85% accuracy, using  a surrounding network of rain gauges at 30-50 Km of distance from the point of study. This research can strengthen various types of research and applications such as ungauged basins research, regional climate modeling, food security early warning systems, agricultural insurance systems, etc.

una forma diferente de ver las series y transformadas de Fourier y como sabemos la transformada de Fourier es un caso particular de la transformada de Laplace por lo que igual funciona, en este método se la solución a la integral principal por medio de integración por partes y se desarrolla un amplio desarrollo de múltiples funciones

In recent years video and image compression have became very required. The availability of powerful software design tools is a fundamental requirement to take advantage of the many advanced and specialized resources included in the latest devices. Video acceleration and processing technologies have become critical for the development of many consumer electronics products. In this paper, we investigate Real Time FPGA implementation of 2-D lifting-based Daubechies 5/3 transforms using a Matlab/Simulink/Xilinx System Generator tool that generates synthesizable VHSIC Hardware Description. This system offers significant advantages: portability, rapid time to market and real time, continuing parametric change in the DWT transform.The proposed model has been designed and simulated using Simulink and System Generator blocks, synthesized with Xilinx Synthesis tool (XST) and implemented on Spartan 3A DSP based XCSD 3400A-4fg476 target device.

Pointwise-supported generalized wavelets are introduced, based on Dirac, doublet and further derivatives of delta. A generalized biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as Laurent Schwartz distributions. A Parseval-like identity is also derived for Taylor series, showing that Taylor series support an energy theorem. New representations for signals called derivagrams are introduced, which are similar to spectrograms. This approach corroborates the impact of wavelets in modern signal analysis.

For functions that are best described in terms of polar coordinates, the two-dimensional Fourier transform can be written in terms of polar coordinates as a combination of Hankel transforms and Fourier series—even if the function does not possess circular symmetry. However, to be as useful as its Cartesian counterpart, a polar version of the Fourier operational toolset is required for the standard operations of shift, multiplication, convolution, etc. This paper derives the requisite polar version of the standard Fourier operations. In particular, convolution—two dimensional, circular, and radial one dimensional—is discussed in detail. It is shown that standard multiplication/convolution rules do apply as long as the correct definition of convolution is applied.
© 2009 Optical Society of America

Analysis of time series used in many areas, one of which is in the field economy. In this research using time series on inflation using Shift Invariant Discrete Wavelet Transform (SIDWT).Time series decomposition using transformation wavelet namely SIDWT with Haar filter and D4. Results of the transformation, coefficient of drag coefficient wavelet and scale that is used for modeling time series. Modeling done by using Multiscale Autoregressive (MAR). In a certain area, inflation to it is an important that he had made the standard-bearer of economic well-being of society, the factors Directors investors in selecting a kind of investment, and the determining factor for the government to formulate policy fiscal, monetary, as well as non-monetary that will be applied. Inflation can be analyzed using methods Shift Invariant Discrete Wavelet Transform (SIDWT) which had been modeled for them to use Mulitiscale Autoregressive (MAR) with the R2 value 93.62%.

All human activity that is directly related to the sea, and the phenomenon coastal tides need information about. Sea tides Sounding in the Central Java city of Semarang a crucial factor in the sector transformation sea or management of the sect in relation to an early warning system and the deluge. Sea tides Information which is accurate, it is very important for the community, especially prone to flooding which was within rob or basin area so that the process done earlier evacuation to a lot of material and the sacrifice and soul can be avoided. Functions wavelet able to represent the functions that are not smooth. This is because base in wavelet is determined by the layout and scale (translation and dilatation). Transformation wavelet there are two kinds, Discrete Wavelet Transform (DWT) and Continue Wavelet Transform (CWT). The use a decomposition wavelet has been growing and is considered more suitable is Maximal Overlap Discrete Wavelet Transform (MODWT). Many coefficient wavelet every level MODWT is always the same, it is different with the method DWT that there is always experienced (decimated) in every increase levels. This nature causes MODWT has the advantage doing time series data modeling. Analysis of data can be concluded tide of Semarang using MODWT acquired MSE at least, the decomposition level 4 and there are many coefficient on that level is 5 with the coefficient determination R2 99.26 %
Keywords : Tides, Wavelet, CWT, DWT, MODWT, Time Series

Particle Swarm Optimizer (PSO) is such a complex stochastic process so that analysis on the stochastic behavior of the PSO is not easy. The choosing of parameters plays an important role since it is critical in the performance of PSO. As far as our investigation is concerned, most of the relevant researches are based on computer simulations and few of them are based on theoretical approach. In this paper, theoretical approach is used to investigate the behavior of PSO. Firstly, a state of PSO is defined in this paper, which contains all the information needed for the future evolution. Then the memory-less property of the state defined in this paper is investigated and proved. Secondly, by using the concept of the state and suitably dividing the whole process of PSO into countable number of stages (levels), a stationary Markov chain is established. Finally, according to the property of a stationary Markov chain, an adaptive method for parameter selection is proposed.

The critical time interval (CTI) is a parameter that has been used to distinguish open-loop from closed-loop control during upright stance. The aim of this study was to develop a new method to determine CTIs. The new approach, termed the intermittent critical time interval (ICTI) method, was motivated from evidence that upright standing is an intermittent rather than an asymptotic stability control process. For this ICTI method, center-of-pressure time series are first transformed to the time–frequency domain with a wavelet method. Subsequently, the CTI is assumed equal to the time span between two local maxima in the time–frequency domain within a distinct frequency band (i.e., 0.5–1.1 Hz). This new method may help facilitate better estimates of the transition time interval between open and closed-loop control during upright stance and can also be applied in future work such as in simulating postural control. In addition, this method can be used in future work to assess temporal changes in CTIs.

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.

This article presents an approach based on state observers to identify the parameters of an unknown periodic force exerted on a mechanical system. This approach comprises two stages and can be executed
in real time by using only displacement measurements. The first stage goal is the estimation of the coefficients of a Fourier series that approximates the periodic force. From the estimated coefficients, the
phase and the amplitude of the signal can be simultaneously computed; and from the estimated force, in a second stage, the frequencies of the signal can be estimated. To perform the tasks at each stage, two state observers were designed. To show the applicability of the proposed approach, the reconstruction of a wave force affecting a marine  structure as well as the computation of the amplitude and phase of its spectral components was taken as case of study. The performance of the state observer was examined by means of  simulations and off-line tests carried out with experimental data. Such data were obtained by executing laboratory tests and measuring waves in the Caribbean sea.

In the last decades, a huge effort has been dedicated to the development of vibration-based techniques for damage detection. In this article, an algorithm based on the wavelet packet transform and the Karhunen–Loéve transform is analysed to perform a pattern recognition application for the structural health monitoring purpose. In this article, the wave-let packet transform is used to decompose the signals coming from an accelerometer on a vibrating composite beam. The configuration of the beam has been changed and the wavelet packet transform was tested as a feature extraction tool. Then the Karhunen–Loéve transform was applied to the data to classify the different patterns and to test its capability of pattern recognition.

In the coming of era the digitized image is an important challenge to deal with the storage and transmission requirements of enormous data, including medical images. Compression is one of the indispensable techniques to solve this problem. In this paper, we propose an algorithm for medical image compression based on lifting base wavelet transform coupled with SPIHT (Set Partition in Hierarchical Trees) coding algorithm, of which we applied the lifting structure to improve the drawbacks of conventional wavelet transform. We compared the results with various wavelet based compression algorithm. Experimental results show that the proposed algorithm is superior to traditional methods for all tested images at low bit rate. Our algorithm provides better PSNR and MSSIM values for medical images only at low bit rate.