On error-spectrum shaping in state-space digital filters

A new scheme for shaping the error spectrum in state-space digital filter structures is proposed. The scheme is based on the application of diagonal second-order error feedback, and can be used in any arbitrary state-space structure having arbitrary order. A method to obtain noise-optimal state-space structures for fixed error feedback coefficients, starting from noise optimal structures in absence of error feedback (the Mullis and Roberts Structures), is also outlined. This optimization is based on the theory of continuous equivalence for state-space structures

A new approach to the realization of low-sensitivity IIR digital filters

A new implementation of an IIR digital filter transfer function is presented that is structurally passive and, hence, has extremely low pass-band sensitivity. The structure is based on a simple parallel interconnection of two all-pass sections, with each section implemented in a structurally lossless manner. The structure shares a number of properties in common with wave lattice digital filters. Computer simulation results verifying the low-sensitivity feature are included, along with results on roundoff noise/dynamic range interaction. A large number of alternatives is available for the implementation of the all-pass sections, giving rise to the well-known wave lattice digital filters as a specific instance of the implementation

A generalized direct-form delta operator-based IIR filter with minimum noise gain and sensitivity

This brief presents the derivation of an arbitrary order delta operator-based direct-form IIR filter with minimum roundoff noise gain and sensitivity. It utilizes the concept of different coupling coefficients at different branch nodes for better noise gain suppression. Two possible structures for realizing the inverse delta operator are considered and procedures for calculating the optimal filter coefficients are given. By means of state-space representation and matrix manipulation, it is also shown that expressions for sensitivity measures of different filter coefficients and their corresponding roundoff noise gain expressions are the same. This enables the simultaneous minimization of sensitivity and noise power for the proposed generalized filter structure.published_or_final_versio

Finite Wordlength Controller Realizations using the Specialized Implicit Form

Une forme d'état implicite spécialisée est présentée pour étudier les effets de l'implantation en précision finie des régulateurs. Cette forme permet une description macroscopique des algorithmes à implanter. Elle constitue un canevas unificateur permettant de décrire les différentes structures utilisées pour l'implantation, telles que les réalisations avec l'opérateur delta, la forme directe II en rho, la forme d'état-observateur et bien d'autres formes qui sont d'habitude traitées séparément dans la littérature. Différentes mesures quantifiant les effets de l'implantation sur le comportement en boucle fermée sont définis dans ce contexte. Elles concernent aussi bien la stabilité que la performance. L'écart entre la réalisation à précision infinie et la réalisation à précision finie est évaluée selon la mesure de sensibilité des coefficients et la mesure du bruit de quantification. Le problème consistant à trouver une réalisation dont l'implantation amène un minimum de dégradation peut alors est résolut numériquement. Cette approche est illustrée avec deux exemples

Optimal realizations of floating-point implemented digital controllers with finite word length considerations.

The closed-loop stability issue of finite word length (FWL) realizations is investigated for digital controllers implemented in floating-point arithmetic. Unlike the existing methods which only address the effect of the mantissa bits in floating-point implementation to the sensitivity of closed-loop stability, the sensitivity of closed-loop stability is analysed with respect to both the mantissa and exponent bits of floating-point implementation. A computationally tractable FWL closed-loop stability measure is then defined, and the method of computing the value of this measure is given. The optimal controller realization problem is posed as searching for a floating-point realization that maximizes the proposed FWL closed-loop stability measure, and a numerical optimization technique is adopted to solve for the resulting optimization problem. Simulation results show that the proposed design procedure yields computationally efficient controller realizations with enhanced FWL closed-loop stability performance

A modified low roundoff digital oscillator design

The work of this thesis is to summarize and compares the existing digital oscillator design methods and combine them to form a modified structure for oscillator design. First of all, a combined structure of complex oscillator design is proposed. The structure combines the advantages of low hardware complexity and low roundoff errors. Then based on the suggested complex oscillator structure, some new digital oscillator structures with uniform frequency spacing are suggested. The new structures are also the modified structure of the existing oscillator. By adding power-of-two shift boxes into the modified structure, dynamic range of the output is enlarged and the quantization errors are greatly reduced. The modified oscillators can generate low frequency and low amplitude sinusoid waves with very small phase and amplitude deviation. In order to further reduce the quantization errors, error feedback circuits is applied into the circuit to further reduce the errors

Finite worldlength effects in fixed-point implementations of linear systems

Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 173-194).by Vinay Mohta.M.Eng

Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)

Oxford, UK, 26 August 200