874 research outputs found
On the inversion of certain nonlinear systems
Journal ArticleAbstract-In this letter, we present some theorems for the exact inversion and the pth-order inversion of a wide class of causal, discrete-time, nonlinear systems. The nonlinear systems we consider are described by the input-output relationship y(n) = g[x(n)]h[x(n - 1); y(n - 1)]+f[x(n - 1); y(n - 1)], where g[•], h[•; •] and f[•; •] are causal, discrete-time and nonlinear operators and the inverse function g-1[•] exists. The exact inverse of such systems is given by z(n) = g-1[{u(n) - f[z(n - 1); u(n -1 )]}/ h[z(n - 1); u(n - 1)]]. Similarly, when h[• ;•] = 1, the pthorder inverse is given by z(n) = gp -1 [u(n)- f[z(n - 1); u(n - 1)]] where gp -1 p [•] is the pth-order inverse of g[•]. Index Terms-Inverse systems, nonlinear filters, nonlinear system
On the inversion of certain nonlinear systems
Journal ArticleIn this letter, we present some theorems for the exact inversion and the pth-order inversion of a wide class of causal, discrete-time, nonlinear systems. The nonlinear systems we consider are described by the input-output relationship y(n) = g[x(n)]h[x(n-1); (n-1)]+f[x(n-1); y(n-1)], here g[], h[; ], and f[; ] are causal, discrete-time and nonlinear operators and the inverse function g-1[.] exists. The exact inverse of such systems is given by z(n) = g-1[fu(n)-f[z(n-1); u(n-1)]g=h[z(n - 1); u(n-1)]]. Similarly, when h[; ] = 1, the pthorder inverse is given by z(n) = g-1 p u(n)-f[z(n-1); u(n-1)]] where g-1 p [.] is the pth-order inverse of g[.]
Volterra and general polynomial related filtering
Journal ArticleThis paper presents a review of polynomial filtering and, in particular, of tlie truncated Volterra filters. Following the introduction of the general properties of such filters, issues such as eficieiit realizations, design, adaptive algoritlims and stability are discussed
Adaptive polynomial filters
Journal ArticleWhile linear filter are useful in a large number of applications and relatively simple from conceptual and implementational view points. there are many practical situations that require nonlinear processing of the signals involved. This article explains adaptive nonlinear filters equipped with polynomial models of nonlinearity. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion, or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. followed by adaptive algorithms using system models involving recursive nonlinear difference equations. Such systems are attractive because they may be able to approximate many nonlinear systems with great parsimony in the use pf coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is also described
Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation
Volterra and polynomial regression models play a major role in nonlinear
system identification and inference tasks. Exciting applications ranging from
neuroscience to genome-wide association analysis build on these models with the
additional requirement of parsimony. This requirement has high interpretative
value, but unfortunately cannot be met by least-squares based or kernel
regression methods. To this end, compressed sampling (CS) approaches, already
successful in linear regression settings, can offer a viable alternative. The
viability of CS for sparse Volterra and polynomial models is the core theme of
this work. A common sparse regression task is initially posed for the two
models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type
algorithm is developed for sparse polynomial regressions. The identifiability
of polynomial models is critically challenged by dimensionality. However,
following the CS principle, when these models are sparse, they could be
recovered by far fewer measurements. To quantify the sufficient number of
measurements for a given level of sparsity, restricted isometry properties
(RIP) are investigated in commonly met polynomial regression settings,
generalizing known results for their linear counterparts. The merits of the
novel (weighted) adaptive CS algorithms to sparse polynomial modeling are
verified through synthetic as well as real data tests for genotype-phenotype
analysis.Comment: 20 pages, to appear in IEEE Trans. on Signal Processin
Lattice and QR decomposition-based algorithms for recursive least squares adaptive nonlinear filters
Journal ArticleThis paper presents a lattice structure for adaptive Volterra systems. The stucture is applicable to arbitrary planes of support of the Volterra kernels. A fast least squares lattice and a fast QR-lattice adaptive nonlinear filtering algorithms based on the lattice structure are also presented. These algorithms share the fast convergence property of fast least squares transversal Volterra filters; however, unlike the transversal filters they do not suffer from numerical instability
Lattice and QR decomposition-based algorithms for recursive least squares adaptive nonlinear filters
Journal ArticleThis paper presents a lattice structure for adaptive Volterra systems. The stucture is applicable to arbitrary planes of support of the Volterra kernels. A fast least squares lattice and a fast QR-lattice adaptive nonlinear filtering algorithms based on the lattice structure are also presented. These algorithms share the fast convergence property of fast least squares transversal Volterra filters; however, unlike the transversal filters they do not suffer from numerical instability
A fast recursive least-squares second order volterra filter
Journal ArticleABSTRACT This paper presents a fast, recursive least-squares (RLS) adaptive nonlinear filter. The nonlinearity is modelled using a second order Volterra series expansion. The structure presented in the paper makes use of the ideas of fast RLS multichannel filters and has a computational complexity of OW3) multiplications. This compares with OW6) multiplications required for direct implementation. Simulation examples in which the filter is employed to identify nonlinear systems using noisy output observations are also presented. Further simplification to the structure through a simplified model is discussed very briefly in the paper
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