Coefficient Sensitivity Properties Research Articles

Two-dimensional delta-operator formulated discrete-time systems: state-space realization and its coefficient sensitivity properties

Delta-operator based implementation of one-dimensional (1-D) discrete-time systems has been the focus of considerable research activity because of its superior finite wordlength properties and possibility of addressing both continuous- and discrete-time systems in a unified manner. We investigate its corresponding two-dimensional (2-D) implementation by introducing the delta-operator based counterpart to the Roesser (1975) local state-space model, the corresponding gramians, and the notion of a balanced realization. The computation of the latter and coefficient sensitivity properties of the resulting implementations are also studied.

Performance advantage of hybrid cascade/parallelhigh order recursive filters

The authors address the performance of a class of IIR digital filter structures that make a compromise between the standard cascade and parallel forms. The structures are easily generated and exhibit improved noise and coefficient sensitivity properties. In this work the authors present the results of bit level, fixed point simulations that demonstrate that the new structures are a superior alternative to the cascade and parallel structures.

Phase sensitivity properties of cascaded digital lattice allpass filters

The phase sensitivity with respect to coefficient errors is studied for a class of lattice digital allpass filters. It is shown that corresponding to each lattice parameter there is a set of frequencies for which the phase response remains invariant to an arbitrary perturbation of the parameter. In addition, a simple result of sensitivity “amplification” in lossless two-pair networks is derived, which is used to obtain means and bounds on the sensitivity functions for these lattice structures in term of the lattice parameters. From these results some useful coefficient sensitivity properties are inferred. A practical example is included to better understand the interaction of sensitivity mechanisms in lattice allpass filter realizations, in the context of transfer functions realized as the parallel connection of two allpass filters. Finally, it is shown that the order reduction process intrinsic to the lattice synthesis procedure minimizes the L ∞ norm of the phase sensitivity at each step.

Wave digital filters based on extracting two‐wire lines

AbstractIt is well known that wave digital filters (WDF's) imitating the behavior of doubly terminated reactance circuits have low coefficient sensitivity properties. Based on the Darlington synthesis procedure, a cascade synthesis of WDF's realizing arbitrary transfer functions has been shown. They are constituted with cascading basic WDF sections corresponding to basic reactance sections. The cascade synthesis procedure, however, is rather complicated in that transmission zeros have to be found by calculating the roots of an algebraic equation.

Applications of wave digital filters to branching filters with low coefficient sensitivity

AbstractWave digital filters made to imitate the behavior of doubly terminated lossless filters (resistance terminated reactance circuits) are a class of digital filters with low coefficient sensitivity. A wave digital filter can realize not only an input‐output transfer function, but also an input reflection coefficient of the doubly terminated lossless filter. However, so far, almost no consideration has been given to the realization of the reflection coefficient by wave digital filters. This paper shows that wave digital filters can be applied to branching filters, narrowband eliminate filters and multibranching filters by utilizing two transfer functions of wave digital filters. Some examples show that these filters composed of wave digital filters can be realized with fewer multipliers and have low coefficient sensitivity properties.

Comparison of the effects of quantization on digital filters

The fixed-point roundoff noise and coefficient sensitivity properties of the cascade canonic, Sedlmeyer-Fettweiss wave digital filter, the digital generalized immittance converter filter, and the Swamy-Thyagarajan wave digital filter are examined. The relative power spectral density and the statistical wordlength of each structure are computed.

An analysis of errors in wave digital filters

The roundoff noise properties of wave digital filters realized with fixed-point arithmetic are studied. The dynamic range of these filters is considered and the effects of scaling on the roundoff noise are deternined. Claimns have been made in the literature concerning the favorable coefficient sensitivity properties of wave digital filters. It is shown that specific configurations of wave digital irdters do exhibit favorable coefficient sensitivity properties, and that filters can be realized winch are insensitive to overall coefficient error at zero frequency (low pass).

Digital formant speech synthesis utilizing wave digital filters

Digital computer processing of speech is of much current interest. This paper examines the synthesis of speech utilizing the wave digital filter which has been shown to have low coefficient sensitivity properties and to generate smaller roundoff error than conventional filters. Also examined is the coefficient quantization in the digital formant speech synthesis model and how implementation with the wave filter may serve as a better alternative. Simulation and generation of speech confirm the feasibility and corresponding advantages of implementation with the wave digital filter compared to conventional filters.

Digital ladder structures and coefficient sensitivity

Recently, there has been a great deal of interest in the implementation of digital filter structures with low-coefficient word length. A conjecture has been made by Fettweis that if digital filter structures are modeled after analog ladder structures, which are known to have desirable coefficient sensitivity properties, then the digital ladder structures will also have these properties and could be implemented with low-coefficient word lengths. To investigate this conjecture, a seventh-order Chebyshev low-pass filter was realized as a digital ladder structure and the coefficient sensitivity was analyzed experimentally under coefficient rounding in floating-point representation. To serve as a comparison similar examples of cascade structures of direct and coupled form sections were also analyzed in the same manner. The conclusions drawn are that, indeed, the digital ladder structures in many cases can be implemented with lower coefficient word lengths than the conventional structures.