Overflow Oscillations Research Articles

On elimination of overflow oscillations in linear time-varying 2-D digital filters represented by a Roesser model

This paper proposes a novel linear matrix inequality (LMI)-based stability criterion to avoid overflow oscillations in 2-D digital filters described by a Roesser state-space model with saturation-type overflow characteristics. In contrast to the conventional approaches, the proposed overflow oscillation elimination methodology can be applied to linear parameter varying time-variant digital filters under overflow subject to both state and output disturbances. For such filters, the proposed criterion ensures the zero-input overflow stability as well as robustness against interferences with a guaranteed H∞ performance bound. A numerical example is presented to demonstrate the effectiveness of the proposed approach.

Passivity and Finite-Gain Performance for Two-Dimensional Digital Filters: The FM LSS Model Case

This brief considers the two-dimensional (2-D) passivity performance analysis problem of 2-D digital filters in the Fornasini–Marchesini local state–space (FM LSS) form. The purpose is to establish a new criterion in terms of linear matrix inequality such that the 2-D digital filters in the FM LSS form ensure 2-D passivity performance with a storage function. Moreover, this brief reveals that the 2-D digital filters exhibit the 2-D finite-gain performance under the proposed criterion. Without interference, the criterion guarantees the asymptotic stability of 2-D digital filters. An application example to a 2-D low-pass filter is given to demonstrate the usefulness of the presented passivity criterion. The criteria in this brief and in a previous work of one of the authors, as a whole, give methodical results for the 2-D passive removal of the overflow oscillation of 2-D digital filters with external inferences.

Condition of the elimination of overflow oscillations in two‐dimensional digital filters with external interference

This study is concerned with the problem of the elimination of overflow oscillations (EOOs) for two-dimensional (2D) digital filters with external interference. The main purpose is the presentation of a new unified criterion such that the underlying 2D digital filter is stable with a positive prescribed interference attenuation level. A performance index is proposed for the first time, which is referred to as generalised dissipativity property. By using this index and two harmonic slack matrices, a novel criterion is established, which can be used to solve ℋ∞ EOOs, passive EOOs and l 2–l ∞ EOOs for 2D digital filters with external interference in a unified framework, and reduce the conservatism of the existing results. The effectiveness of the criterion is demonstrated by a numerical example.

Overflow Oscillation Elimination of 2-D Digital Filters in the Roesser Model with Wiener Process Noise

Recently, Ahn's criteria were proposed for dealing with deterministic external interference with finite energy in two-dimensional (2-D) digital filters. However, these criteria fail for cases where the 2-D filters have stochastic noise. In this letter, we propose a new criterion for overflow oscillation elimination of 2-D digital filters in the Roesser model with Wiener process noise. The criterion guarantees the asymptotic stability as well as a 2-D expected power bound. Thus, it can ascertain the attenuation of the effect of Wiener process noise to a prescribed level. This criterion is also expressed by linear matrix inequality (LMI). A numerical example is provided to show the usefulness of the proposed result.

L 2 − l ∞ stability criterion for fixed-point state-space digital filters with saturation nonlinearity

This article proves that there exists an l 2 − l ∞ stability criterion for fixed-point state-space digital filters without overflow oscillations. By the l 2 − l ∞ stability property, this new criterion guarantees asymptotic stability and attenuates the effect of external interference to a prescribed l 2 − l ∞-induced norm bound. We represent this stability criterion as the form of linear matrix inequality, which can be solved easily using the existing numerical packages. Finally, we present an illustrative example, which shows the effectiveness of the proposed stability criterion.

$l_{2} - l_{\infty}$ Elimination of Overflow Oscillations in 2-D Digital Filters Described by Roesser Model With External Interference

Two-dimensional (2-D) digital filters can be corrupted by external interferences, but no stability criteria have yet been established. This brief proposes a new <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> stability criterion for the absence of limit cycles in 2-D digital filters that are described by Roesser model with external interference. Our new criterion ensures the attenuation of the effect of external interference on 2-D digital filters to a prescribed level. This criterion also guarantees the asymptotic stability result without external interference. The proposed criterion is represented in terms of linear matrix inequality, which can be verified by using existing numerical packages. We use an illustrative example to demonstrate the effectiveness of the proposed criterion.

Two-dimensional digital filters described by Roesser model with interference attenuation

To the present time, stability criteria have been proposed for one-dimensional digital filters with external interference, but no stability criterion exists for cases where two-dimensional digital filters have external interference. In this paper, we propose a new criterion for the elimination of overflow oscillations in two-dimensional digital filters described by Roesser model with saturation arithmetic and external interference. This criterion ensures asymptotic stability with a guaranteed H~ performance. The proposed criterion is represented in terms of linear matrix inequality (LMI); thus, it is computationally efficient. Illustrative examples are given to demonstrate the effectiveness of the proposed criterion.

Improved criterion for the elimination of overflow oscillations in digital filters with external disturbance

In this paper, an improved criterion for the elimination of overflow oscillations in digital filters with external disturbance is presented. Compared with some existing results in Ahn (AEU, Int. J. Electron. Commun. 65:750-752, 2011) and Kokil et al. (AEU, Int. J. Electron. Commun. doi:10.1016/j.aeue.2012.01.004, 2012), a distinct feature of the proposed criterion is that it can include the existing results as special cases or be less restrictive than them. Finally, an example is given to show this improvement over the existing conditions.

2-D digital filter realization without overflow oscillations

A novel criterion for the elimination of overflow oscillations in 2-D state-space digital filters described by the Roesser model employing two’s complement overflow arithmetic is presented. The criterion takes the form of linear matrix inequality (LMI) and, hence, is computationally tractable. The criterion is a generalization and improvement over an earlier criterion. An example shows the effectiveness of the new criterion.

A new condition for the elimination of overflow oscillations in direct form digital filters

This article proposes a new condition for the elimination of overflow oscillations in direct form digital filters with external interference. This condition reduces the effect of external interference to an ℋ∞ norm constraint. When there is no external interference, this condition ensures exponential stability. Moreover, this condition guarantees that the state vector is bounded if the external interference is bounded. The proposed condition is represented by linear matrix inequality (LMI), which can be checked easily by standard numerical packages. A numerical example is given to show the effectiveness of the proposed condition.

Induced l∞ stability of fixed-point digital filters without overflow oscillations and instability due to finite word length effects

This article studies a new criterion for the induced l∞ stability of fixed-point state-space digital filters without overflow oscillations and instability due to finite word length effects. The criterion not only guarantees exponential stability but also reduces the effect of external interference to an induced l∞ norm constraint. We present a numerical example, which demonstrates the effectiveness of the proposed criterion.

A note on the criterion for the elimination of overflow oscillations in fixed-point digital filters with saturation arithmetic and external disturbance

A recently reported criterion for the exponential stability and H∞ performance of fixed-point digital filters with saturation arithmetic and external disturbance is reviewed. It is shown that there is a technical error in this criterion. A corrected version of the criterion is presented. Finally, a relaxed version of the criterion is made available.

Criterion for the elimination of overflow oscillations in fixed-point digital filters with saturation arithmetic and external disturbance

Abstract In this paper, a new criterion for the H ∞ elimination of overflow oscillations in fixed-point digital filters with saturation arithmetic and external disturbance is presented. The criterion not only guarantees exponential stability but also reduces the effect of external disturbance to an H ∞ norm constraint. The criterion takes the form of linear matrix inequality (LMI) and, hence, is computationally tractable. An illustrative example is given to demonstrate the effectiveness of the proposed criterion.

Comment on “Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic: An LMI approach” by V. Singh [Digital Signal Process. 16 (2006) 45–51

A recently reported criterion for the elimination of overflow oscillations in fixed-point state-space digital filters employing saturation arithmetic is reviewed. It is shown that this criterion is not new and can be obtained directly from a previously reported criterion as a special case.

Elimination of overflow oscillations in direct form digital filters using saturation arithmetic

A novel frequency-domain criterion for the elimination of limit cycles in a class of digital filters using saturation arithmetic is presented. An example showing the effectiveness of the present criterion is given.

Comments on ‘New LMI condition for the nonexistence of overflow oscillations in 2-D state-space digital filters using saturation arithmetic’

A recently reported criterion for the nonexistence of overflow oscillations in two-dimensional (2-D) digital filters described by the Roesser model employing saturation arithmetic is reviewed. It is shown that this criterion is not new and can be obtained directly from a previously reported criterion as a special case.

An LMI based criterion for the nonexistence of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic

A linear matrix inequality (LMI) based criterion for the nonexistence of overflow oscillations in fixed-point state-space digital filters employing saturation arithmetic is presented. The criterion turns out to be an improvement over previously reported LMI based criteria.

Optimal Synthesis of a Class of 2-D Digital Filters with Minimum L2-Sensitivity and No Overflow Oscillations

The minimization problem of an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints is formulated for a class of two-dimensional (2-D) state-space digital filters. First, the problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algorithm with closed-form formula for gradient evaluation. The coordinate transformation matrix obtained is then used to synthesize the optimal 2-D state-space filter structure that minimizes the L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints. Finally, a numerical example is presented to illustrate the utility of the proposed technique.

A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic

In [Singh V. Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic. IEEE Trans Circ Syst 1990;37(6):814–8], a frequency-domain criterion for the suppression of limit cycles in fixed-point state-space digital filters using saturation overflow arithmetic was presented. The passivity property owing to the presence of multiple saturation nonlinearities was exploited therein. In the present paper, a new notion of passivity, namely, that involving the state variables is considered, thereby arriving at an entirely new frequency-domain criterion for the suppression of limit cycles in such filters.

New LMI condition for the nonexistence of overflow oscillations in 2-D state-space digital filters using saturation arithmetic

A new criterion for the nonexistence of overflow oscillations in 2-D state-space digital filters described by Roesser model using saturation arithmetic is presented. The criterion is in the form of a linear matrix inequality (LMI) and hence computationally tractable. The criterion is compared with an earlier LMI-based criterion due to Xiao and Hill. It turns out that the present criterion may uncover some new A (i.e., other than those arrived at via Xiao–Hill's criterion) for which the absence of overflow oscillations is assured.