Enhancement of Calcifications in Mammograms using Volterra Series based Quadratic Filter

The paper summarizes the design and implementation of a quadratic edge detection filter, based on Volterra series, for enhancing calcifications in mammograms. The proposed filter can account for much of the polynomial nonlinearities inherent in the input mammogram image and can replace the conventional edge detectors like Laplacian, gaussian etc. The filter gives rise to improved visualization and early detection of microcalcifications, which if left undetected, can lead to breast cancer. The performance of the filter is analyzed and found superior to conventional spatial edge detectors

Damage detection in nonlinear structures using discrete-time volterra series

Structural damage identification is basically a nonlinear phenomenon; however, nonlinear procedures are not used currently in practical applications due to the complexity and difficulty for implementation of such techniques. Therefore, the development of techniques that consider the nonlinear behavior of structures for damage detection is a research of major importance since nonlinear dynamical effects can be erroneously treated as damage in the structure by classical metrics. This paper proposes the discrete-time Volterra series for modeling the nonlinear convolution between the input and output signals in a benchmark nonlinear system. The prediction error of the model in an unknown structural condition is compared with the values of the reference structure in healthy condition for evaluating the method of damage detection. Since the Volterra series separate the response of the system in linear and nonlinear contributions, these indexes are used to show the importance of considering the nonlinear behavior of the structure. The paper concludes pointing out the main advantages and drawbacks of this damage detection methodology. © (2013) Trans Tech Publications.

Identification of nonlinear structures using discrete-time Volterra series

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Model updating of the non-linear vibrating structures through Volterra series and proper orthogonal decomposition

Classical procedures for model updating in non-linear mechanical systems based on vibration data can fail because the common linear metrics are not sensitive for non-linear behavior caused by gaps, backlash, bolts, joints, materials, etc. Several strategies were proposed in the literature in order to allow a correct representative model of non-linear structures. The present paper evaluates the performance of two approaches based on different objective functions. The first one is a time domain methodology based on the proper orthogonal decomposition constructed from the output time histories. The second approach uses objective functions with multiples convolutions described by the first and second order discrete-time Volterra kernels. In order to discuss the results, a benchmark of a clamped-clamped beam with an pre-applied static load is simulated and updated using proper orthogonal decomposition and Volterra Series. The comparisons and discussions of the results show the practical applicability and drawbacks of both approaches.

Nonlinear features identified by Volterra series for damage detection in a buckled beam

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-parametric identification of a non-linear buckled beam using discrete-time Volterra Series

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Characterization of the nonlinear behavior of a F-16 aircraft using discrete-time Volterra series

The linearity assumption in the structural dynamics analysis is a severe practical limitation. Further, in the investigation of mechanisms presented in fighter aircrafts, as for instance aeroelastic nonlinearity, friction or gaps in wing-load-payload mounting interfaces, is mandatory to use a nonlinear analysis technique. Among different approaches that can be used to this matter, the Volterra theory is an interesting strategy, since it is a generalization of the linear convolution. It represents the response of a nonlinear system as a sum of linear and nonlinear components. Thus, this paper aims to use the discrete-time version of Volterra series expanded with Kautz filters to characterize the nonlinear dynamics of a F-16 aircraft. To illustrate the approach, it is identified and characterized a non-parametric model using the data obtained during a ground vibration test performed in a F-16 wing-to-payload mounting interfaces. Several amplitude inputs applied in two shakers are used to show softening nonlinearities presented in the acceleration data. The results obtained in the analysis have shown the capability of the Volterra series to give some insight about the nonlinear dynamics of the F-16 mounting interfaces. The biggest advantage of this approach is to separate the linear and nonlinear contributions through the multiple convolutions through the Volterra kernels.

Application of Volterra series in nonlinear mechanical system identification and in structural health monitoring problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Impact of reduced complexity inverse Volterra series transfer function-based nonlinear equalizer in coherent OFDM systems for next-generation core networks

A modern electronic nonlinearity equalizer (NLE) based on inverse Volterra series transfer function (IVSTF) with reduced complexity is applied on coherent optical orthogonal frequency-division multiplexing (CO-OFDM) signals for next-generation long- and ultra-long-haul applications. The OFDM inter-subcarrier crosstalk effects are explored thoroughly using the IVSTF-NLE and compared with the case of linear equalization (LE) for transmission distances of up to 7000 km. © 2013 IEEE.

Volterra-based reconfigurable nonlinear equalizer for coherent OFDM

A reconfigurable nonlinear equalizer (RNLE) based on inverse Volterra series transfer function is proposed for dual-polarization (DP) and multiband coherent optical orthogonal frequency-division multiplexing (OFDM) signals. It is shown that the RNLE outperforms by 2 dB the linear equalization in a 260-Gb/s DP-OFDM system at 1500 km. The RNLE improves the tolerance to inter/intraband nonlinearities, being independent on polarization tributaries, modulation format, signal bit rate, subcarrier number, and distance. © 1989-2012 IEEE.

Numerical analysis of artificial neural network and volterra-based nonlinear equalizers for coherent optical OFDM

One major drawback of coherent optical orthogonal frequency-division multiplexing (CO-OFDM) that hitherto remains unsolved is its vulnerability to nonlinear fiber effects due to its high peak-to-average power ratio. Several digital signal processing techniques have been investigated for the compensation of fiber nonlinearities, e.g., digital back-propagation, nonlinear pre- and post-compensation and nonlinear equalizers (NLEs) based on the inverse Volterra-series transfer function (IVSTF). Alternatively, nonlinearities can be mitigated using nonlinear decision classifiers such as artificial neural networks (ANNs) based on a multilayer perceptron. In this paper, ANN-NLE is presented for a 16QAM CO-OFDM system. The capability of the proposed approach to compensate the fiber nonlinearities is numerically demonstrated for up to 100-Gb/s and over 1000km and compared to the benchmark IVSTF-NLE. Results show that in terms of Q-factor, for 100-Gb/s at 1000km of transmission, ANN-NLE outperforms linear equalization and IVSTF-NLE by 3.2dB and 1dB, respectively.

Experimental comparison of artificial neural network and volterra based nonlinear equalization for CO-OFDM

A novel artificial neural network (ANN)-based nonlinear equalizer (NLE) of low complexity is demonstrated for 40-Gb/s CO-OFDM at 2000 km, revealing ∼1.5 dB enhancement in Q-factor compared to inverse Volterra-series transfer function based NLE.

A new low-power highly linear mixer design using differential derivative superposition

This paper presents the analysis and design of a new low power and highly linear mixer topology based on a newly reported differential derivative superposition method. Volterra series and harmonic balance are employed to investigate its linearisation mechanism and to optimise the design. A prototype mixer has been designed and is being implemented in 0.18μm CMOS technology. Simulation shows this mixer achieves 19.7dBm IIP3 with 10.5dB conversion gain, 13.2dB noise figure at 2.4GHz and only 3.8mW power consumption. This performance is competitive with already reported mixers.

Design and optimization next generation passive all-optical networks

Este trabalho investiga novas metodologias para as redes óticas de acesso de próxima geração (NG-OAN). O trabalho está dividido em quatro tópicos de investigação: projeto da rede, modelos numéricos para efeitos não lineares da fibra ótica, impacto dos efeitos não lineares da fibra ótica e otimização da rede. A rede ótica de acesso investigada nesse trabalho está projetado para suprir os requisitos de densidade de utilizadores e cobertura, isto é, suportar muitos utilizadores ( 1000) com altas velocidades de conexão dedicada ( 1 Gb/s) ocupando uma faixa estreita do espectro ( 25 nm) e comprimentos de fibra ótica até 100 km. Os cenários são baseados em redes óticas passivas com multiplexagem por divisão no comprimento de onda de alta densidade (UDWDM-PON) utilizando transmissores/receptores coerentes nos terminais da rede. A rede é avaliada para vários ritmos de transmissão usando formatos de modulação avançados, requisitos de largura de banda por utilizador e partilha de banda com tecnologias tradicionais de redes óticas passivas (PON). Modelos numéricos baseados em funções de transferência das séries de Volterra (VSTF) são demonstrados tanto para a análise dos efeitos não lineares da fibra ótica quanto para avaliação do desempenho total da rede. São apresentadas as faixas de potência e distância de transmissão nas quais as séries de Volterra apresentam resultados semelhantes ao modelo referência Split-Step Fourier (SSF) (validado experimentalmente) para o desempenho total da rede. Além disso, um algoritmo, que evita componentes espectrais com intensidade nulo, é proposto para realizar cálculos rápidos das séries. O modelo VSTF é estendido para identificar unicamente os efeitos não lineares da fibra ótica mais relevantes no cenário investigado: Self-Phase Modulation (SPM), Cross-Phase Modulation (XPM) e Four-Wave Mixing (FWM). Simulações numéricas são apresentadas para identificar o impacto isolado de cada efeito não linear da fibra ótica, SPM, XPM e FWM, no desempenho da rede com detecção coerente UDWDM-PON, transportando canais com modulação digital em fase (M-ária PSK) ou modulação digital em amplitude (M-ária QAM). A análise numérica é estendida para diferentes comprimentos de fibra ótica mono modo (SSMF), potência por canal e ritmo de transmissão por canal. Por conseguinte, expressões analíticas são extrapoladas para determinar a evolução do SPM, XPM e FWM em função da potência e distância de transmissão em cenários NG-OAN. O desempenho da rede é otimizada através da minimização parcial da interferência FWM (via espaçamento desigual dos canais), que nesse caso, é o efeito não linear da fibra ótica mais relevante. Direções para melhorias adicionas no desempenho da rede são apresentados para cenários em que o XPM é relevante, isto é, redes transportando formatos de modulação QAM. A solução, nesse caso, é baseada na utilização de técnicas de processamento digital do sinal.

Quadratic Predictor based Differential Encoding and Decoding of Speech Signals

Modeling nonlinear systems using Volterra series is a century old method but practical realizations were hampered by inadequate hardware to handle the increased computational complexity stemming from its use. But interest is renewed recently, in designing and implementing filters which can model much of the polynomial nonlinearities inherent in practical systems. The key advantage in resorting to Volterra power series for this purpose is that nonlinear filters so designed can be made to work in parallel with the existing LTI systems, yielding improved performance. This paper describes the inclusion of a quadratic predictor (with nonlinearity order 2) with a linear predictor in an analog source coding system. Analog coding schemes generally ignore the source generation mechanisms but focuses on high fidelity reconstruction at the receiver. The widely used method of differential pnlse code modulation (DPCM) for speech transmission uses a linear predictor to estimate the next possible value of the input speech signal. But this linear system do not account for the inherent nonlinearities in speech signals arising out of multiple reflections in the vocal tract. So a quadratic predictor is designed and implemented in parallel with the linear predictor to yield improved mean square error performance. The augmented speech coder is tested on speech signals transmitted over an additive white gaussian noise (AWGN) channel.