A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

On the Range of the Fourier Transform Associated with the Spherical Mean Operator

We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.

Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM

We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats).

On generalized orlicz sequence spaces of Fourier coefficients for trigonometric gap series. I.

We investigate the operator associating with a function fєLp2π, 1Fourier coefficients of ƒ with respect to a trigonometric gap system, as well as an operator from a modular space X ρs(ϕ) to the generalized Orlicz sequence space lϕ.

On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

MSC 2010: 42A32; 42A20

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Nonlinear Fourier transform for optical communications

The nonlinear Fourier transform, also known as eigenvalue communications, is a transmission and signal processing technique that makes positive use of the nonlinear properties of fibre channels. I will discuss recent progress in this field.

Optical communication based on the periodic nonlinear Fourier transform signal processing

In this work we introduce the periodic nonlinear Fourier transform (PNFT) and propose a proof-of-concept communication system based on it by using a simple waveform with known nonlinear spectrum (NS). We study the performance (addressing the bit-error-rate (BER), as a function of the propagation distance) of the transmission system based on the use of the PNFT processing method and show the benefits of the latter approach. By analysing our simulation results for the system with lumped amplification, we demonstrate the decent potential of the new processing method.

Fault diagnosis scheme for open-circuit faults in switched reluctance motor drives using fast Fourier transform algorithm with bus current detection

Reliability of power converters is of crucial importance in switched reluctance motor drives used for safety-critical applications. Open-circuit faults in power converters will cause the motor to run in unbalanced states, and if left untreated, they will lead to damage to the motor and power modules, and even cause a catastrophic failure of the whole drive system. This study is focused on using a single current sensor to detect open-circuit faults accurately. An asymmetrical half-bridge converter is considered in this study and the faults of single-phase open and two-phase open are analysed. Three different bus positions are defined. On the basis of a fast Fourier transform algorithm with Blackman window interpolation, the bus current spectrums before and after open-circuit faults are analysed in details. Their fault characteristics are extracted accurately by the normalisations of the phase fundamental frequency component and double phase fundamental frequency component, and the fault characteristics of the three bus detection schemes are also compared. The open-circuit faults can be located by finding the relationship between the bus current and rotor position. The effectiveness of the proposed diagnosis method is validated by the simulation results and experimental tests.

Proteção diferencial de transformadores de potência utilizando a transformada Wavelet

About 10% of faults involving the electrical system occurs in power transformers. Therefore, the protection applied to the power transformers is essential to ensure the continuous operation of this device and the efficiency of the electrical system. Among the protection functions applied to power transformers, the differential protection appears as one of the main schemes, presenting reliable discrimination between internal faults and external faults or inrush currents. However, when using the low frequency components of the differential currents flowing through the transformer, the main difficulty of the conventional methods of differential protection is the delay for detection of the events. However, internal faults, external faults and other disturbances related to the transformer operation present transient and can be appropriately detected by the wavelet transform. In this paper is proposed the development of a wavelet-based differential protection for detection and identification of external faults to the transformer, internal faults, and transformer energizing by using the wavelet coefficient energy of the differential currents. The obtained results reveal the advantages of using of the wavelet transform in the differential protection compared to conventional protection, since it provides reliability and speed in detection of these events.

Estimação de potência em tempo real utilizando a transformada wavelet

The goal of the power monitoring in electrical power systems is to promote the reliablility as well as the quality of electrical power.Therefore, this dissertation proposes a new theory of power based on wavelet transform for real-time estimation of RMS voltages and currents, and some power amounts, such as active power, reactive power, apparent power, and power factor. The appropriate estimation the of RMS and power values is important for many applications, such as: design and analysis of power systems, compensation devices for improving power quality, and instruments for energy measuring. Simulation and experimental results obtained through the proposed MaximalOverlap Discrete Wavelet Transform-based method were compared with the IEEE Standard 1459-2010 and the commercial oscilloscope, respectively, presenting equivalent results. The proposed method presented good performance for compact mother wavelet, which is in accordance with real-time applications.

Classificador máquina de suporte vetorial com análise de Fourier aplicada em dados de EEG e EMG

The classifier support vector machine is used in several problems in various areas of knowledge. Basically the method used in this classier is to end the hyperplane that maximizes the distance between the groups, to increase the generalization of the classifier. In this work, we treated some problems of binary classification of data obtained by electroencephalography (EEG) and electromyography (EMG) using Support Vector Machine with some complementary techniques, such as: Principal Component Analysis to identify the active regions of the brain, the periodogram method which is obtained by Fourier analysis to help discriminate between groups and Simple Moving Average to eliminate some of the existing noise in the data. It was developed two functions in the software R, for the realization of training tasks and classification. Also, it was proposed two weights systems and a summarized measure to help on deciding in classification of groups. The application of these techniques, weights and the summarized measure in the classier, showed quite satisfactory results, where the best results were an average rate of 95.31% to visual stimuli data, 100% of correct classification for epilepsy data and rates of 91.22% and 96.89% to object motion data for two subjects.

Sistema inteligente para o processamento de imagens digitais intrabucais oclusais

Several are the areas in which digital images are used in solving day-to-day problems. In medicine the use of computer systems have improved the diagnosis and medical interpretations. In dentistry it’s not different, increasingly procedures assisted by computers have support dentists in their tasks. Set in this context, an area of dentistry known as public oral health is responsible for diagnosis and oral health treatment of a population. To this end, oral visual inspections are held in order to obtain oral health status information of a given population. From this collection of information, also known as epidemiological survey, the dentist can plan and evaluate taken actions for the different problems identified. This procedure has limiting factors, such as a limited number of qualified professionals to perform these tasks, different diagnoses interpretations among other factors. Given this context came the ideia of using intelligent systems techniques in supporting carrying out these tasks. Thus, it was proposed in this paper the development of an intelligent system able to segment, count and classify teeth from occlusal intraoral digital photographic images. The proposed system makes combined use of machine learning techniques and digital image processing. We first carried out a color-based segmentation on regions of interest, teeth and non teeth, in the images through the use of Support Vector Machine. After identifying these regions were used techniques based on morphological operators such as erosion and transformed watershed for counting and detecting the boundaries of the teeth, respectively. With the border detection of teeth was possible to calculate the Fourier descriptors for their shape and the position descriptors. Then the teeth were classified according to their types through the use of the SVM from the method one-against-all used in multiclass problem. The multiclass classification problem has been approached in two different ways. In the first approach we have considered three class types: molar, premolar and non teeth, while the second approach were considered five class types: molar, premolar, canine, incisor and non teeth. The system presented a satisfactory performance in the segmenting, counting and classification of teeth present in the images.

Sistema inteligente para o processamento de imagens digitais intrabucais oclusais

Several are the areas in which digital images are used in solving day-to-day problems. In medicine the use of computer systems have improved the diagnosis and medical interpretations. In dentistry it’s not different, increasingly procedures assisted by computers have support dentists in their tasks. Set in this context, an area of dentistry known as public oral health is responsible for diagnosis and oral health treatment of a population. To this end, oral visual inspections are held in order to obtain oral health status information of a given population. From this collection of information, also known as epidemiological survey, the dentist can plan and evaluate taken actions for the different problems identified. This procedure has limiting factors, such as a limited number of qualified professionals to perform these tasks, different diagnoses interpretations among other factors. Given this context came the ideia of using intelligent systems techniques in supporting carrying out these tasks. Thus, it was proposed in this paper the development of an intelligent system able to segment, count and classify teeth from occlusal intraoral digital photographic images. The proposed system makes combined use of machine learning techniques and digital image processing. We first carried out a color-based segmentation on regions of interest, teeth and non teeth, in the images through the use of Support Vector Machine. After identifying these regions were used techniques based on morphological operators such as erosion and transformed watershed for counting and detecting the boundaries of the teeth, respectively. With the border detection of teeth was possible to calculate the Fourier descriptors for their shape and the position descriptors. Then the teeth were classified according to their types through the use of the SVM from the method one-against-all used in multiclass problem. The multiclass classification problem has been approached in two different ways. In the first approach we have considered three class types: molar, premolar and non teeth, while the second approach were considered five class types: molar, premolar, canine, incisor and non teeth. The system presented a satisfactory performance in the segmenting, counting and classification of teeth present in the images.

Utilização da transformada de wavelet para detecção de variações anormais de tensão em sistemas elétricos com geração distribuída

The increasing demand in electricity and decrease forecast, increasingly, of fossil fuel reserves, as well as increasing environmental concern in the use of these have generated a concern about the quality of electricity generation, making it well welcome new investments in generation through alternative, clean and renewable sources. Distributed generation is one of the main solutions for the independent and selfsufficient generating systems, such as the sugarcane industry. This sector has grown considerably, contributing expressively in the production of electricity to the distribution networks. Faced with this situation, one of the main objectives of this study is to propose the implementation of an algorithm to detect islanding disturbances in the electrical system, characterized by situations of under- or overvoltage. The algorithm should also commonly quantize the time that the system was operating in these conditions, to check the possible consequences that will be caused in the electric power system. In order to achieve this it used the technique of wavelet multiresolution analysis (AMR) for detecting the generated disorders. The data obtained can be processed so as to be used for a possible predictive maintenance in the protection equipment of electrical network, since they are prone to damage on prolonged operation under abnormal conditions of frequency and voltage.