Some new results on the stability of direct-form digital filters with finite wordlength nonlinearities

2015 ◽  
Vol 108 ◽  
pp. 549-557 ◽  
Author(s):  
Choon Ki Ahn
Keyword(s):  
Digital Filters ◽  
Direct Form ◽  
The Stability

New results for the realization of interfered direct-form digital filters with single two's complement nonlinearity

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mani Kant Kumar ◽  
Nishant Jha
Keyword(s):  
Design Methodology ◽  
Digital Filters ◽  
Linear Matrix ◽  
Sufficient Criterion ◽  
External Disturbances ◽  
Content Type ◽  
Direct Form ◽  
The Stability ◽  
Output Information ◽  
First Time

PurposeThis paper deals with the problem of input/output-to-state stability (IOSS) of direct-form digital filters, which simultaneously contain external disturbances and two's complement nonlinearity. The nonlinearity under consideration is confined to the sector [–1, 1], which contains saturation, zeroing, two's complement and triangular.Design/methodology/approachThe proposed condition is based on IOSS approach, which is capable of providing a framework for checking and analysing the stability of nonlinear system based on input as well as output information.FindingsA linear matrix inequality (LMI)-based new sufficient criterion for the IOSS of the suggested system is obtained. The obtained criterion is capable of detecting the output-to-state stability (OSS) and asymptotic stability of direct-form digital filters with zero external disturbances. In addition, state-norm estimator for the filter under consideration is constructed by adopting an exponential-decay IOSS criterion. Several examples are provided to illustrate the usefulness of the proposed criteria.Originality/valueThe result of the paper is introduced for the first time, and it is suitable for stability analysis of interfered direct-form digital filter with two's complement overflow using IOSS approach.

An improved criterion for peak-to-peak realization of direct-form interfered digital filters employing saturation nonlinearities

2015 ◽  
Vol 34 (3) ◽  
pp. 996-1010 ◽  
Author(s):  
Priyanka Kokil ◽  
Swapnil Sadashiv Shinde
Keyword(s):  
Asymptotic Stability ◽  
State Space ◽  
Digital Filters ◽  
Practical Importance ◽  
External Interference ◽  
Content Type ◽  
Discrete Signals ◽  
Attenuation Level ◽  
Direct Form ◽  
Saturation Arithmetic

Purpose – The purpose of this paper is to present a criterion for global asymptotic stability of state-space direct-form digital filters employing saturation arithmetic. Design/methodology/approach – An elegant use of induced l ∞ approach (also known as a peak-to-peak approach) is made to develop a criterion for the overflow stability of state-space direct-form digital filters. Findings – The criterion not only guarantees asymptotic stability but also reduces the effect of external interference. The presented method yields better interference attenuation level as compared to a recently reported method. Numerical examples are given to illustrate the effectiveness of the proposed method. Practical implications – Digital filters are important dynamical systems in signal processing which are used for the processing of discrete signals. During the implementation of higher-order digital filter in hardware or software, introduction of external interference is unavoidable. Therefore, stability analysis of digital filters in the presence of external interference is of much practical importance. Originality/value – The main result of the paper is reported for the first time and it is useful to establish the asymptotic stability of digital filters in the presence of external disturbances.

GA-BASED DESIGN OF 2D STATE-SPACE DIGITAL FILTERS WITH LINEAR PHASE CHARACTERISTICS

2007 ◽  
Vol 16 (02) ◽  
pp. 287-303 ◽  
Author(s):  
SANG-CHURL NAM ◽  
MASAHIDE ABE ◽  
MASAYUKI KAWAMATA
Keyword(s):  
State Space ◽  
Design Problem ◽  
Digital Filters ◽  
Design Method ◽  
Design Procedure ◽  
Gray Code ◽  
Superior Performance ◽  
Magnitude Response ◽  
The Stability ◽  
Group Delays

This paper proposes a GA-based design method for two-dimensional (2D) state-space digital filters which satisfy simultaneously the magnitude response and constant group delays. The design problem of 2D state-space digital filters is formulated subject to the constraint that the resultant filters are stable. To apply the genetic algorithm to the design problem, all coefficients of 2D state-space digital filters are encoded into the Gray code representation demonstrating the superior performance to the standard binary one. In addition, a stability test routine is embedded in the design procedure in order to ensure the stability for the resultant filters. A numerical example is given to demonstrate the effectiveness of the proposed method.

Stability-Guaranteed Two-Phase Design of Odd-Order Variable-Magnitude Digital Filters

2016 ◽  
Vol 26 (02) ◽  
pp. 1750033
Author(s):  
Tian-Bo Deng
Keyword(s):  
Transfer Function ◽  
Digital Filter ◽  
Digital Filters ◽  
Tuning Parameter ◽  
Second Phase ◽  
Variable Model ◽  
Odd Order ◽  
Order Variable ◽  
The Stability ◽  
Fifth Order

Guaranteeing the stability is one of the most critical issues in designing a variable recursive digital filter. In this paper, we first present an odd-order recursive variable model (transfer function) that is used for designing an odd-order variable-magnitude (VM) digital filter, and then we replace the original coefficients of the denominator of the odd-order transfer function with a set of new parameters. These new parameters can ensure that they can take arbitrary values without incurring instability of the designed odd-order VM filter. To make the VM filter coefficients variable, we find all the VM filter coefficients as polynomial functions of the tuning parameter, which includes two phases. The first phase designs a set of recursive digital filters with fixed coefficients (constant filters), and the second phase utilizes a curve-fitting scheme to represent each coefficient as a polynomial function. As a result, the VM filter coefficients become variable, and the proposed parameter-substitution-based denominator coefficients ensure the filter stability. This is the most important contribution of the parameter-substitution-based design scheme. This paper uses the fifth-order demonstrative example to verify the stability guarantee as well as the design accuracy of the obtained the fifth-order VM filter.

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