The properties of digital all-pass filters are reviewed and a broad overview of the diversity of applications in digital filtering is provided. Starting with the definition and basic properties of a scalar all-pass function, a variety of structures satisfying the all-pass property are assembled, with emphasis placed on the concept of structural losslessness. Applications are then outlined in notch filtering, complementary filtering and filter banks, multirate filtering, spectrum and group-delay equalization, and Hilbert transformations. In all cases, the structural losslessness property induces very robust performance in the face of multiplier coefficient quantization. Finally, the state-space manifestations of the all-pass property are explored, and it is shown that many all-pass filter structures are devoid of limit cycle behavior and feature very low roundoff noise gain. >

/pdf/the-digital-all-pass-filter-a-versatile-signal-processing-593kdqvx76.pdf

The digital all-pass filter: a versatile signal processing building block

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

/pdf/finite-wordlength-effects-in-digital-filters-a-review-34933zf3yj.pdf

Finite wordlength effects in digital filters : a review

A review is presented of recent work on quantization and overflow effects in digital filters. These unwanted non-linear 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.

Finite wordlength in digital filters: A review

Digital filters with hypercomplex coefficients are considered. This filter can reduce the order of filters to 1/4 of a filter with real coefficients. The fact that digital filters with hypercomplex coefficients of the first order can realize any order of digital filters with real coefficients less than 4 is described in detail. Three different realizations of arbitrary higher-order digital filter with real coefficients are also considered. Stability criteria for digital filters with hypercomplex coefficients are suggested. >

Digital filters with hypercomplex coefficients

Realization of High Accuracy 2-D Variable IIR Digital Filters

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.

T. Saramaki

Papers

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