Multistage Volterra Filters

lIntroductionVolterrafiltershavebeenusedinmanycommunicationproblems,suchaschannelequaliZation[2],13]andechocancellation[4].AnoptimalVolterrafiltercanbedeterminedbyusingsimilartechniquesforoptimizinglinearfilters.Theadaptivealgorithmsforiterativelydet...     

Filtered-X second-order Volterra adaptive algorithms

The authors propose filtered-X second-order Volterra adaptive algorithms based on a multichannel structure application to active noise control. The developed algorithms can be used as alternatives in the case where the standard filtered-X LMS algorithm does not perform well     

Adaptive second-order Volterra delay filter

A new adaptive second-order Volterra delay filter is developed to include the linear and quadratic filter coefficients for system modelling and identification. The filter structure is very effective in modelling second-order Volterra systems with sparse system coefficients     

Adaptive parallel-cascade truncated Volterra filters

This paper studies adaptive truncated Volterra filters employing parallel-cascade structures. Parallel-cascade realizations implement higher order Volterra systems as a parallel connection of multiplicative combinations of lower order truncated Volterra systems. A normalized LMS adaptive filter is developed, and its performance capabilities are evaluated using a series of simulation experiments. The experimental results indicate that the normalized LMS adaptive parallel-cascade Volterra filter has superior convergence properties over several competing structures. This paper also includes an experiment that demonstrates the capability of the parallel-cascade adaptive system to reduce its implementation complexity by using fewer than the maximum number of branches required for the most general realization of the system     

Volterra kernels in nonlinear systems

A general expression for the functional expansion of an operator corresponding to a pth-order Volterra kernel is obtained. This expansion eliminates the use of special algorithms, such as those developed by Van Trees, for the optimum synthesis of nonlinear control systems.     

Semisystolic implementation of second-order Volterra digital filters based on recurrence algorithm of Volterra filtering

The letter presents a quasitriangular semisystolic array for the implementation of nonlinear second-order volterra digital filters. The performance of the proposed systolic array is based on the recurrence algorithm of Volterra filtering, which is also derived here.<>     

Modified Volterra series transfer function method

In this letter, we offer a modified version of the Volterra series transfer function (VSTF) method that has been previously proposed as an analytical solution to the nonlinear Schrodinger equation for single-mode fibers. The modified VSTF provides a simple closed-form expression of the output of a mildly nonlinear fiber. It gives orders more accurate result than the original VSTF method and can successfully solve the energy divergence problem experienced by the original method. The result is a stronger analytical tool for modeling signal propagation in optical communication systems     

Signal modelling through adaptive Volterra representations

In adaptive Volterra signal modelling, the recursive implementations of the method of least squares commonly employ a weighting factor which has constraints. Here, the least squares estimation is reformulated as a constrained optimisation problem and solved using the Lagrange programming neural networks. The weighting factor is adapted and found to be optimal     

Efficient implementation of the Volterra filter

An efficient implementation of the Volterra filter is presented which uses a frequency domain representation to reduce the number of computations. The multidimensional convolution of the Volterra filter is transformed to the frequency domain giving a transformed input matrix which is sparse and obtained directly from a one-dimensional Fourier transform, in addition to the sparse nature of the transformed input matrix, symmetries in both the Volterra filter and the frequency domain representation are exploited to increase the efficiency of the algorithm. The computational saving is demonstrated by comparing it with the direct implementation of the time domain representation and another technique which uses a frequency domain representation but does not utilise symmetry     

Volterra series representation of time-frequency distributions

This paper addresses a Volterra series representation of bilinear (or quadratic) time-frequency distributions that belong to Cohen's class, whereby the analogy of the bilinear class with a second-order double Volterra series is utilized. In addition, a different viewpoint for the bilinear kernel and a complementary interpretation concerning the quadratic time-frequency distributions are provided.     

Multisource discrimination using IIR Volterra filtering

This paper exhibits an algorithm based on Volterra-type processing in order to detect several independent sources on the same carrier frequency and to determine the number of them. The use of infinite impulse response (IIR) Volterra filtering to build a suitable discrimination test is dictated by the need of higher-order moments in this type of nonlinear problem, as well as the need of IIR for convergence     

一种全解耦的Volterra自适应滤波器

本文研究了Volterra自适应滤波的解耦问题.通过对Volterra滤波器的伪线性组合结构的提出和分析,得到了一个新的关于均方误差MSE的表达式,并将Volterra自适应滤波问题描述为一个约束优化问题,从而导出了满足最小均方误差(MMSE)指标的具有分块对角型输入相关矩阵的全解耦Volterra标准方程,据此设计了一种全解耦的Volterra自适应滤波器,给出了滤波器权向量的自适应修正公式.仿真结果验证了本文方法的有效性.     

Volterra filtering and higher order whiteness

Some properties of Volterra filtering are established. Finite-order, finite-horizon Volterra filtering is investigated as well as its asymptotic properties. Next, the concepts of Volterra unpredictability and uninterpolability lead to generalizations of the notion of white noise to higher orders. These generalizations are introduced and relations are established between them     

Efficient algorithms for Volterra system identification

In this paper, nonlinear filtering and identification based on finite-support Volterra models are considered. The Volterra kernels are estimated via input-output statistics or directly in terms of input-output data. It is shown that the normal equations for a finite-support Volterra system excited by zero mean Gaussian input have a unique solution if, and only if, the power spectral process of the input signal is nonzero at least at m distinct frequencies, where m is the memory of the system. A multichannel embedding approach is introduced. A set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format. Efficient algorithms for the estimation of the Volterra parameters are derived for batch, as well as for adaptive processing. An efficient order-recursive method is presented for the determination of the Volterra model structure. The proposed methods are illustrated by simulations     

Discrete-Space Volterra Series Representations with Truncation Bounds

We give a Volterra-series representation theorem for discrete-space input-output maps that are analytic. The theorem provides a bound on the error in approximating the series with its first p + 1 terms. Examples are given to illustrate how the theorem can be used.     

Equivalent Low-Pass Representations for Bandpass Volterra Systems

Relationships are derived for finding equivalent low-pass representations of the Volterra kernels corresponding to a widely used model for a nonlinear communication channel. The results are a logical extension of the usual complex envelope representation for bandpass signals. The equivalent low-pass representations are useful for simplifying calculations in cases where the input and output signals of the system are bandpass.     

一种新的非线性Volterra优化算法

文章提出了非线性信号处理中"绝对贡献因子"的概念,并在此基础上提出了"基于绝对贡献因子的自适应Volterra优化算法",该算法能够较好的区分非线性扩展向量中的冗余项和最优项,优化后的算法能够使其计算量减小30%左右。     

基于Volterra级数预测的音频频带扩展

 本文采用非线性分析方法,基于Volterra级数提出了一种宽带音频信号的频带扩展方法,并利用高斯混合模型(Gaussian Mixture Model,GMM)和码本映射技术对扩展后的音频信号进行了谱包络和能量增益调整.实验表明,所提算法的性能要好于已有的非线性频带扩展算法,当用本文的方法替代ITU-T G.722.1C编码器中的噪声填充技术时,在24kbps得到了提升的超宽带音频质量.     

Volterra series transfer function of single-mode fibers

A nonrecursive Volterra series transfer function (VSTF) approach for solving the nonlinear Schrodinger (NLS) wave equation for a single-mode optical fiber is presented. The derivation of the VSTF is based on expressing the NLS equation In the frequency domain and retaining the most significant terms (Volterra kernels) in the resulting transfer function. Due to its nonrecursive property and closed-form analytic solution, this method can excel as a tool for designing optimal optical communication systems and lumped optical equalizers to compensate for effects such as linear dispersion, fiber nonlinearities and amplified spontaneous emission (ASE) noise from optical amplifiers. We demonstrate that a third-order approximation to the VSTF model compares favorably with the split-step Fourier (recursive) method in accuracy for power levels used in current optical communication systems. For higher power levels, there is a potential for improving the accuracy by including higher-order Volterra kernels at the cost of increased computations. Single-pulse propagation and the interaction between two pulses propagating at two different frequencies are also analyzed with the Volterra method to verify the ability to accurately model nonlinear effects. The analysis can be easily extended to include inter-channel interference in multi-user systems like wavelength-division multiple-access (WDM), time-division multiplexed (TDM), or code-division multiplexed (CDM) systems