Criterion for the H∞ Suppression of Overflow Oscillations in Fixed Point Digital Filters Employing Saturation Nonlinearities and External Interference

This paper proposes a novel criterion for suppressing the [Formula: see text] overflow oscillations in fixed point state-space digital filters employing saturation nonlinearities and external interference. The proposed criterion can be used to ensure the exponential stability (ES) and diminish the external interference effects to an [Formula: see text] norm constraint. An example is given to exemplify the utility of the obtained results.

Overflow oscillation-free realization of digital filters with saturation

Purpose The purpose of this paper is to establish a criterion for the global asymptotic stability of fixed-point state–space digital filters using saturation overflow arithmetic. Design/methodology/approach The method of stability analysis used in this paper is the second method of Lyapunov. The approach in this paper makes use of a precise upper bound of the state vector of the system and a novel passivity property associated with the saturation nonlinearities. Findings The presented criterion leads to an enhanced stability region in the parameter-space as compared to several existing criteria. Practical implications When dealing with the design of fixed-point state–space digital filters, it is desirable to have a criterion for selecting the filter coefficients so that the designed filter becomes free of overflow oscillations. The criterion presented in this paper provides enhanced saturation overflow stability region and therefore facilitates the designer greater flexibility in selecting filter parameters for overflow oscillation-free realization of digital filters. Originality/value The approach uses the structural properties of the saturation nonlinearities in a greater detail. The exploitation of upper bound of the system state vector together with a new passivity property of saturation nonlinearities is a unique feature of the present approach. The presented approach may lead to results not covered by several existing approaches.

Novel Results for Induced l∞ Stability for Digital Filters with External Noise

This paper establishes novel criteria for the induced [Formula: see text] stability to avoid overflow oscillations in fixed-point digital filters with generalized overflow non-linearities and external noise. The proposed linear matrix inequality (LMI)-based criteria ensure exponential stability as well as confirm reduction in the influence of external noise. The generalized overflow non-linearities which are considered for analysis commonly occur in practice, viz. saturation, zeroing, two's complement, and triangular. The presented approach unifies a string of existing results which are derived by considering saturation non-linearities and external interference. Simulation examples are shown to validate the usefulness of the proposed approach.

Analysis of Memory Effects in Digital Filters with Overflow Arithmetic

<p>This paper deals with the problem of undesired memory effects in nonlinear digital<br />filters owing to the influence of past excitations on future outputs. The nonlinearities under consideration cover the usual types of overflow arithmetic employed in practice. Based on the Hankel norm performance, a new criterion is proposed to ensure the reduction of undesired memory effects in digital filters with overflow arithmetic. In absence of external input, the nonexistence of overflow oscillations is also confirmed by the proposed criterion. A numerical example together with simulation result showing the effectiveness of the criterion is given.</p>

Criterion for limit cycle-free state-space digital filters with external disturbances and generalized overflow non-linearities

This paper investigates the problem of [Formula: see text] elimination of overflow oscillations in fixed-point state-space digital filters using generalized overflow non-linearities and external disturbance. The generalized overflow non-linearities under consideration cover the common types of overflow arithmetic used in practice, for instance zeroing, two’s complement, triangular and saturation. New criteria are established to ensure not only exponential stability, but also reduction in the effect of external disturbance to an [Formula: see text] norm constraint. The obtained criteria are in linear matrix inequality (LMI) framework and, hence, are computationally tractable. The presented approach constitutes a generalization over several previously reported approaches for the [Formula: see text] elimination of overflow oscillations. For saturation non-linearities, the presented result turns out to be less conservative than several existing criteria. Numerical examples are provided to demonstrate the effectiveness of the presented approach.