Wave digital filters (WDFs) are modeled after classical filters, preferably in lattice or ladder configurations or generalizations thereof. They have very good properties concerning coefficient accuracy requirements, dynamic range, and especially all aspects of stability under finite-arithmetic conditions. A detailed review of WDF theory is given. For this several goals are set: to offer an introduction for those not familiar with the subject, to stress practical aspects in order to serve as a guide for those wanting to design or apply WDFs, and to give insight into the broad range of aspects of WDF theory and its many relationships with other areas, especially in the signal-processing field. Correspondingly, mathematical analyses are included only if necessary for gaining essential insight, while for all details of more special nature reference is made to existing literature.

Wave digital filters: Theory and practice

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

A new realization of recursive digital filters based on a cascade of complex all-pass structures is proposed. The cascade realization ensures low stopband sensitivity, whereas the all-pass sections, being structurally bounded, guarantee low passband sensitivity. The proposed structure can exactly realize any elliptic transfer function, and it is easy to derive the multiplier coefficients associated with this structure from the original transfer function expression. To reduce the computational complexity, some of the coefficients are rounded to integer values and an optimum approximation to the original transfer function is obtained by using a minimax optimization procedure. Several examples show that the proposed structure requires significantly fewer bits than other known cascade-form realizations. Another advantage of the proposed structure is that it is free of overflow oscillations.

Very low sensitivity realization of IIR digital filters using a cascade of complex all-pass structures

Three classes of digital-filter structures, namely two classes of cascade structures and one class of wave structures, are compared with regards to the number of arithmetic operations, the inherent speed capability, the output noise due to product quantization, and the sensitivity to multiplier-coefficient quantization Four types of filters are considered, namely a Butterworth low-pass filter, a Chebyshev high-pass filter, an elliptic bandstop filter, and an elliptic band-pass filter The arithmetic is assumed to be of the fixed-point type, numbers are assumed to be in two's complement representation, and number quantization is assumed to be by rounding

A comparison of cascade and wave fixed-point digital-filter structures

A systematic and exhaustive procedure is used to generate a class of new low-sensitivity second-order digital-filter structures which are amenable to error-spectrum shaping (ESS). Collectively, these structures can realize any stable second-order transfer function. For every transfer function, a choice of at least two structures is available but, through a sensitivity analysis, the optimum one can always be identified. The paper concludes with sensitivity and roundoff-noise comparisons which show that the new structures are usually superior relative to corresponding direct canonic structures and also relative to the state-space section-optimal structure.

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Low-sensitivity digital-filter structures which are amenable to error-spectrum shaping

By using the concept of the generalised-immittance convertor, new 2nd-order digital-filter sections are developed. These are then used as building blocks in a cascade synthesis. The proposed synthesis yields lowpass, highpass and bandstop filters with improved inband signal/noise ratio relative to that in conventional cascade filters. In addition, it yields low-noise and economical digital equalisers.

M.G. Rezk

Papers

Digital-filter synthesis using concept of generalised-immittance convertor

A comparison of cascade and wave fixed-point digital-filter structures

Corrigendum: Digital-filter synthesis using concept of generalised-immittance converter