Roundoff Noise in Floating Point Digital Filters

Rao, Bhaskar D.

doi:10.1016/s0090-5267(96)80039-9

Cited by 4 publications

(2 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The quantization error effect on digital filters resulting from the finite precision using floating-point arithmetic has been fairly extensively studied over the last four decades (for example, Sandberg 1967, Liu and Kaneko 1969, Kan and Aggarwal 1971, Kaneko and Liu 1971, Liu 1971, Zeng and Neuvo 1991, Smith et al 1992, Rao 1996, Bomar et al 1997, Tsai 1997, Ko and Bitmead 2004, see Kontro et al (1992) for a review. The effect of coefficient rounding in floating-point arithmetic seems first to have been considered by Kaneko and Liu (1971) (see also Liu 1971), who analysed the sensitivity of the filter poles and the sensitivity of the frequency response to multiplicative perturbations on the coefficients for several filter structures.…”

Section: Introductionmentioning

confidence: 99%

Optimal controller and filter realizations using finite-precision, floating-point arithmetic

Whidborne

et al. 2005

International Journal of Systems Science

View full text Add to dashboard Cite

The problem of reducing the fragility of digital controllers and filters implemented using finite-precision, floating-point arithmetic is considered. Floating-point arithmetic parameter uncertainty is multiplicative, unlike parameter uncertainty resulting from fixed-point arithmetic. Based on first-order eigenvalue sensitivity analysis, an upper bound on the eigenvalue perturbations is derived. Consequently, open-loop and closed-loop eigenvalue sensitivity measures are proposed. These measures are dependent upon the filter/controller realization. Problems of obtaining the optimal realization with respect to both the open-loop and the closed-loop eigenvalue sensitivity measures are posed. The problem for the open-loop case is completely solved. Solutions for the closed-loop case are obtained using non-linear programming. The problems are illustrated with a numerical example.

show abstract

Section: Introductionmentioning

confidence: 99%

Optimal controller and filter realizations using finite-precision, floating-point arithmetic

Whidborne

et al. 2005

International Journal of Systems Science

View full text Add to dashboard Cite

show abstract

“…Overflow or underflow occurs when the bits for the exponent part are not sufficient. The effects of finite-precision floating-point implementation have been well studied in digital filter designs (Kallioja¨rvi and Astola 1996, Rao 1996, Ralev and Bauer 1999. However, there has been relatively little work studying explicitly floating-point digital controller implementations.…”

Section: Introductionmentioning

confidence: 99%

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

Chen

Whidborne

et al. 2004

International Journal of Control

View full text Add to dashboard Cite

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 floatingpoint 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.

show abstract

Implementation of a Class of Low Complexity, Low Sensitivity Digital Controllers Using Adaptive Fixed-Point Arithmetic

Williamson¹

2001

Digital Controller Implementation and Fragility

View full text Add to dashboard Cite

Roundoff Noise in Floating Point Digital Filters

Cited by 4 publications

References 27 publications

Optimal controller and filter realizations using finite-precision, floating-point arithmetic

Optimal controller and filter realizations using finite-precision, floating-point arithmetic

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

Implementation of a Class of Low Complexity, Low Sensitivity Digital Controllers Using Adaptive Fixed-Point Arithmetic

Contact Info

Product

Resources

About