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

Photometric and spectroscopic study of the intermediate-age open cluster NGC 2355

In this paper we analyse the evolutionary status and properties of the old open cluster NGC 2355, located in the Galactic anticentre direction, as a part of the long term programme BOCCE. NGC 2355 was observed with LBC@LBT using the Bessel $B$, $V$, and $I_c$ filters. The cluster parameters have been obtained using the synthetic colour-magnitude diagram (CMD) method, as done in other papers of this series. Additional spectroscopic observations with FIES@NOT of three giant stars were used to determine the chemical properties of the cluster. Our analysis shows that NGC 2355 has metallicity slightly less than solar, with [Fe/H]$=-0.06$ dex, age between 0.8 and 1 Gyr, reddening $E(B-V)$ in the range 0.14 and 0.19 mag, and distance modulus $(m-M)_0$ of about 11 mag. We also investigated the abundances of O, Na, Al, $\alpha$, iron-peak, and neutron capture elements, showing that NGC 2355 falls within the abundance distribution of similar clusters (same age and metallicity). The Galactocentric distance of NGC~2355 places it at the border between two regimes of metallicity distribution; this makes it an important cluster for the study of the chemical properties and evolution of the disc.Comment: 20 pages, 11 figures, Accepted on MNRA

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

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Large Binocular Telescope observations of PSR J2043+2740

We present the results of deep optical imaging of the radio/$\gamma$-ray pulsar PSR J2043+2740, obtained with the Large Binocular Telescope (LBT). With a characteristic age of 1.2 Myr, PSR J2043+2740 is one of the oldest (non recycled) pulsars detected in $\gamma$-rays, although with still a quite high rotational energy reservoir ($\dot{E}_{\rm rot} = 5.6 \times 10^{34}$ erg s$^{-1}$). The presumably close distance (a few hundred pc), suggested by the hydrogen column density ($N_{\rm H} \lesssim 3.6 \times 10^{20}$ cm$^{-2}$), would make it a viable target for deep optical observations, never attempted until now. We observed the pulsar with the Large Binocular Camera of the LBT. The only object (V=25.44$\pm$0.05) detected within ~3" from the pulsar radio coordinates is unrelated to it. PSR J2043+2740 is, thus, undetected down to V~26.6 (3-$\sigma$), the deepest limit on its optical emission. We discuss the implications of this result on the pulsar emission properties.Comment: 4 pages, 3 figures, accepted for publication on MNRA