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

Sufficient stability bounds for slowly varying direct-form recursive linear filters and their applications in adaptive IIR filters

Journal ArticleAbstract-This correspondence derives a sufficient time-varying bound on the maximum variation of the coefficients of an exponentially stable time-varying direct-form homogeneous linear recursive filter. The stability bound is less conservative than all previously derived bounds for time-varying IIR systems. The bound is then applied to control the step size of output-error adaptive IIR filters to achieve bounded-input bounded-output (BIBO) stability of the adaptive filter. Experimental results that demonstrate the good stability characteristics of the resulting algorithms are included. This correspondence also contains comparisons with other competing output-error adaptive IIR filters. The results indicate that the stabilized method possesses better convergence behavior than other competing techniques

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[.]

Equalization of recursive polynomial systems

Journal ArticleAbstract-This letter presents some theorems for the exact and pth-order equalization of nonlinear systems described by recursive polynomial input-output relationships. It is shown that the nonlinear equalizers derived on the basis of this theory have simple and computationally efficient structures. Furthermore, the pth-order equalizers can be shown to operate in a stable manner for a finite range of values of the input amplitude when the linear component of the nonlinear system being equalized has minimum phase properties

ADAPTIVE AND NONLINEAR SIGNAL PROCESSING

1996/1997X Ciclo1967Versione digitalizzata della tesi di dottorato cartacea

Analysis of Different Low Complexity Nonlinear Filters for Acoustic Echo Cancellation

Linear filters are often employed in most signal processing applications. As a matter of fact, they are well understood within a uniform theory of discrete linear systems. However, many physical systems exhibit some nonlinear behaviour, and in certain situations linear filters perform poorly. One case is the problem of acoustic echo cancellation, where the digital filter employed has to identify as close as possible the acoustic echo path that is found to be highly nonlinear. In this situation a better system identification can be achieved by a nonlinear filter. The problem is to find a nonlinear filter structure able to realize a good approximation of the echo path without any significant increase of the computational load. Conventional Volterra filters are well suited for modelling that system but they generally need too many computational resources for a real time implementation. In this paper we consider some low complexity nonlinear filters in order to find out a filter structure able to achieve performances close to those of the Volterra filter, but with a reduced increase of the computational load in comparison to the linear filters commonly employed in commercial acoustic echo cancellers

Analysis of Different Low Complexity Nonlinear Filters for Acoustic Echo Cancellation

Linear filters are often employed in most signal processing applications. As a matter of fact, they are well understood within a uniform theory of discrete linear systems. However, many physical systems exhibit some nonlinear behaviour, and in certain situations linear filters perform poorly. One case is the problem of acoustic echo cancellation, where the digital filter employed has to identify as close as possible the acoustic echo path that is found to be highly nonlinear. In this situation a better system identification can be achieved by a nonlinear filter. The problem is to find a nonlinear filter structure able to realize a good approximation of the echo path without any significant increase of the computational load. Conventional Volterra filters are well suited for modelling that system but they generally need too many computational resources for a real time implementation. In this paper we consider some low complexity nonlinear filters in order to find out a filter structure able to achieve performances close to those of the Volterra filter, but with a reduced increase of the computational load in comparison to the linear filters commonly employed in commercial acoustic echo cancellers

Nonlinear Signal and Image Processing—a special issue in honour of Giovanni L. Sicuranza on his seventy-fifth birthday

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