A classification is given of the various possible nonlinear effects that can occur in recursive digital filters due to signal quantization and adder overflow. The effects include limit cycles, overflow oscillations, and quantization noise. A review is given of recent literature on this subject. Alternative methods of avoiding some of these nonlinear phenomena are discussed.

Effects of quantization and overflow in recursive digital filters

Recently a method (RASCAL) for determining graph similarity using a maximum common edge subgraph algorithm has been proposed which has proven to be very efficient when used to calculate the relative similarity of chemical structures represented as graphs. This paper describes heuristics which simplify a RASCAL similarity calculation by taking advantage of certain properties specific to chemical graph representations of molecular structure. These heuristics are shown experimentally to increase the efficiency of the algorithm, especially at more distant values of chemical graph similarity.

Heuristics for similarity searching of chemical graphs using a maximum common edge subgraph algorithm

The problem of solving the optimal (minimum-noise) error feedback coefficients for recursive digital filters is addressed in the general high-order case. It is shown that when minimum noise variance at the filter output is required, the optimization problem leads to set of familiar Wiener-Hopf or Yule-Walker equations, demonstrating that the optimal error feedback can be interpreted as a special case of Wiener filtering. As an alternative to the optimal solution, the formulas for suboptimal error feedback with symmetric or antisymmetric coefficients are derived. In addition, the design of error feedback using power-of-two coefficients is discussed. The efficiency of high order error feedback is examined by test implementations of the set of standard filters. It is concluded that error feedback is a very powerful and versatile method for cutting down the quantization noise in any classical infinite impulse response (IIR) filter implemented as a cascade of second-order direct form sections. The high-order schemes are attractive for use with high-order direct form sections. >

Noise reduction in recursive digital filters using high-order error feedback

Error spectrum shaping (ESS) can significantly reduce finite-wordlength error in recursive fixed-point digital filters. Most past work on ESS has focused on second-order filters. In this paper, expressions for the ESS coefficients minimizing the roundoff error are derived for high-order filters composed of cascaded second-order sections. A comparison of the noise gains is made between optimal and suboptimal ESS structures and the section-optimal structure; the ESS structures perform well in comparison. A heuristic section-ordering strategy, based on ideas underlying ESS, is proposed and deemed useful, particularly for elliptic filters.

Optimal and suboptimal error spectrum shaping for cascade-form digital filters

A review is presented of recent work on quantization and overflow effects in digital filters. These unwanted nonlinear phenomena include parasitic oscillations (limit cycles) and quantization noise. Modern stabilization methods and noise optimization strategies are discussed~ A comprehensive bibliographY contains the relevant original contributions dealing with the analysis of various finite wordlength effects and measures to reduce or avoid them. Butterweck, H.J. and J.H.F. Ritzerfeld, M.J. Werter FINITE WORDLENGTH EFFECTS IN DIGITAL FILTERS: A review. Faculty of Electrical Engineering, Eindhoven University of Technology, The Netherlands, 1988. EUT Report 88-E-205 The authors are with the Group Electromagnetism and Circuit Theory, Faculty of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 ME EINDHOVEN, The Netherlands

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Finite wordlength effects in digital filters : a review

In digital filters, nonlinear phenomena caused by adder overflow can occur. Some of these phenomena that have been observed in a 2nd-order recursive digital filter are mentioned. A circuit is described in which the error produced by overflow is delayed and fed back into the filter. It is shown that this circuit improves the overflow behaviour.

Improvement of overflow behaviour of 2nd-order digital filters by means of error feedback

Owing to the nonlinear behaviour of the adders in a digital filter, certain phenomena such as limit cycles and jumps may occur. The possibility of the jump phenomenon occurring in digital filters is studied. Sufficient conditions for a special 2nd-order filter are given.

Jump phenomenon in digital filters

A method for measuring bandwidth is described It has been shown that, for a stationary narrowband Gaussian process, the relative bandwidth squared is proportional to the probability of a negative maximum By using digital techniques for counting and sorting maximum points, a bandwidth meter has been built

L. Kristiansson

Papers

Improvement of overflow behaviour of 2nd-order digital filters by means of error feedback

Jump phenomenon in digital filters

Method for measuring the relative bandwidth of a narrowband Gaussian process