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.

Estudo sobre a detecção de invariância de escala discreta em sistemas com criticalidade auto-organizada

Recent studies have shown evidence of log-periodic behavior in non-hierarchical systems. An interesting fact is the emergence of such properties on rupture and breakdown of complex materials and financial failures. These may be examples of systems with self-organized criticality (SOC). In this work we study the detection of discrete scale invariance or log-periodicity. Theoretically showing the effectiveness of methods based on the Fourier Transform of the log-periodicity detection not only with prior knowledge of the critical point before this point as well. Specifically, we studied the Brazilian financial market with the objective of detecting discrete scale invariance in Bovespa (Bolsa de Valores de S˜ao Paulo) index. Some historical series were selected periods in 1999, 2001 and 2008. We report evidence for the detection of possible log-periodicity before breakage, shown its applicability to the study of systems with discrete scale invariance likely in the case of financial crashes, it shows an additional evidence of the possibility of forecasting breakage

Síntese e caracterização de materiais mesoporosos para a captura de CO2: influência do óxido de níquel

Several materials are currently under study for the CO2 capture process, like the metal oxides and mixed metal oxides, zeolites, carbonaceous materials, metal-organic frameworks (MOF's) organosilica and modified silica surfaces. In this work, evaluated the adsorption capacity of CO2 in mesoporous materials of different structures, such as MCM-48 and SBA- 15 without impregnating and impregnated with nickel in the proportions 5 %, 10 % and 20 % (m/m), known as 5Ni-MCM-48, 10Ni-MCM-48, 20Ni-MCM-48 and 5Ni-SBA-15, 10NiSBA-15, 20Ni-SBA-15. The materials were characterized by means of X-ray diffraction (XRD), thermal analysis (TG and DTG), Fourier transform infrared spectroscopy (FT-IR), N2 adsorption and desorption (BET) and scanning electron microscopy (SEM) with EDS. The adsorption process was performed varying the pressure of 100 - 4000 kPa and keeping the temperature constant and equal to 298 K. At a pressure of 100 kPa, higher concentrations of adsorption occurred for the materials 5Ni-MCM-48 (0.795 mmol g-1 ) and SBA-15 (0.914 mmol g-1 ) is not impregnated, and at a pressure of 4000 kPa for MCM-48 materials (14.89 mmol g-1) and SBA-15 (9.97 mmol g-1) not impregnated. The results showed that the adsorption capacity varies positively with the specific area, however, has a direct dependency on the type and geometry of the porous structure of channels. The data were fitted using the Langmuir and Freundlich models and were evaluated thermodynamic parameters Gibbs free energy and entropy of the adsorption system

Uso de metamaterial em antenas de microfita com supercondutor

Metamaterials have attracted great attention in recent decades, due to their electromagnetic properties which are not found in nature. Since metamaterials are now synthesized by the insertion of artificially manufactured inclusions in a specified homogeneous medium, it became possible for the researcher to work with a wide collection of independent parameters, for example, the electromagnetic properties of the material. An investigation of the properties of ring resonators was performed as well as those of metamaterials. A study of the major theories that clearly explain superconductivity was presented. The BCS theory, London Equations and the Two-Fluid Model are theories that support the application of superconducting microstrip antennas. Therefore, this thesis presents theoretical, numerical and experimental-computational analysis using full-wave formalism, through the application of the Transverse Transmission Line – LTT method applied in the Fourier Transform Domain (FTD). The LTT is a full wave method, which, as a rule, obtains the electromagnetic fields in terms of the transverse components of the structure. The inclusion of the superconducting patch is performed using the complex resistive boundary condition. Results of resonant frequency as a function of antenna parameters are obtained. To validate the analysis, computer programs were developed using Fortran, simulations were created using the commercial software, with curves being drawn using commercial software and MATLAB, in addition to comparing the conventional patch with the superconductor as well as comparing a metamaterial substrate with a conventional one, joining the substrate with the patch, observing what improves on both cas

Encapsulamento de solventes em nanotubos de haloisita para promoção de auto-reparo em polímeros

Micro cracking during service is a critical problem in polymer structures and polymer composite materials. Self-healing materials are able to repair micro cracks, thus their preventing propagation and catastrophic failure of structural components. One of the self-healing approaches presented in the literature involves the use of solvents which react with the polymer. The objective of this research is to investigate a procedure to encapsulate solvents in halloysite nanotubes to promote self-healing ability in epoxy. Healing is triggered by crack propagation through embedded nanotubes in the polymer, which then release the liquid sovent into the crack plane. Two solvents were considered in this work: dimethylsulfoxide (DMSO) and nitrobenzene. The nanotubes were coated using the layer-by-layer technique of oppositely charged polyelectrolytes: cetyltrimethylammonium bromide (CTAB) and sodium polyacrylate. Solvent encapsulation was verified by X-ray diffraction (XRD), Fourier transform infrared (FTIR), analysis thermogravimetry (TGA), adsorption and desorption of nitrogen and scanning electron microscopy (SEM). The introduction of the solvent DMSO into the cavity of the nanotubes was confirmed by the techniques employed. However, was not verified with nitrobenzene only promoted clay aggregation. The results suggest that the CTAB reacted with the halloystite to form a sealing layer on the surface of the nanotubes, thus encapsulating the solvent, while this was not verified using sodium polyacrylate.

Detecção e diagnostico de agarramento em válvulas posicionadoras

Valve stiction, or static friction, in control loops is a common problem in modern industrial processes. Recently, many studies have been developed to understand, reproduce and detect such problem, but quantification still remains a challenge. Since the valve position (mv) is normally unknown in an industrial process, the main challenge is to diagnose stiction knowing only the output signals of the process (pv) and the control signal (op). This paper presents an Artificial Neural Network approach in order to detect and quantify the amount of static friction using only the pv and op information. Different methods for preprocessing the training set of the neural network are presented. Those methods are based on the calculation of centroid and Fourier Transform. The proposal is validated using a simulated process and the results show a satisfactory measurement of stiction.