First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book.

Wavelets and Subband Coding

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

This paper presents a tutorial review of lattice structures and their use for adaptive prediction of time series Lattice filters associated with stationary covariance sequences and their properties are discussed The least squares prediction problem is defined for the given data case, and it is shown that many of the currently used lattice methods are actually approximations to the stationary least squares solution The recently developed class of adaptive least squares lattice algorithms are described in detail, both in their unnormalized and normalized forms The performance of the adaptive least squares lattice algorithm is compared to that of some gradient adaptive methods Lattice forms for ARMA processes, for joint process estimation, and for the sliding-window covariance case are presented The use of lattice structures for efficient factorization of covariance matrices and solution of Toeplitz sets of equations is briefly discussed

Lattice filters for adaptive processing

The evolution of CORDIC, an iterative arithmetic computing algorithm capable of evaluating various elementary functions using a unified shift-and-add approach, and of CORDIC processors is reviewed. A method to utilize a CORDIC processor array to implement digital signal processing algorithms is presented. The approach is to reformulate existing DSP algorithms so that they are suitable for implementation with an array performing circular or hyperbolic rotation operations. Three categories of algorithm are surveyed: linear transformations, digital filters, and matrix-based DSP algorithms. >

CORDIC-based VLSI architectures for digital signal processing

In this paper, quadrature mirror filters (QMF) are reviewed. After a brief introduction to multirate building blocks, the two-band QMF bank is discussed. Various distortions caused by the structure, and methods to eliminate these distortions are outlined. Perfect-reconstruction structures for the two-band case are reviewed, and the results are extended to the case of arbitrary number of channels. The relation between perfect-reconstruction QMF banks and the concept of losslessness in transfers-matrices is indicated. New lattice structures are presented, which perform the perfect reconstruction, sometimes even under coefficient quantization.

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Quadrature mirror filter banks, M-band extensions and perfect-reconstruction techniques

Symmetric wave digital filters derived from reference filters in lattice configuration require, in general, fewer multipliers. They can be designed with excellent pass-band sensitivity properties. Their theory is easily established by using results from the scattering parameter theory of classical symmetric filters. Numerical results obtained by computer simulation are presented.

Wave digital lattice filters

Two basic properties of wave digital filters, their property of requiring fewer digits for the multiplier coefficients (to which the property of roundoff noise reduction is related) and their stability, had so far only been inferred from certain analogies with unit element filters. These properties are now proved in a direct way by introducing the concepts of pseudopower, pseudopassivity, and pseudolosslessness, corresponding to the familiar concepts of power, passivity, and losslessness in classical circuits.

Pseudo-passivity, sensitivity, and stability of wave digital filters

Parasitic oscillations can occur in digital filters due to the granularity of the signal and to overflow. It is shown that for wave digital filters, the earlier concept of pseudopower leads to a function called stored pseudopower, from which a simple criterion guaranteeing absence of parasitic oscillations can be derived. For fixed-point two's-complement arithmetic, this criterion can be taken into account by particularly simple requirements for the adaptor output signals. A special type of calculus is developed which makes it possible to derive the corresponding simple requirements for the chopping operations at the various stages of the signal processing in the adaptors. The method is extended to cover scaling.

Suppression of parasitic oscillations in wave digital filters

The adders and multipliers of a wave digital filter (WDF) can be grouped into n-port building blocks called adaptors. Various aspects concerning the realization of adaptors are discussed. These include the minimization of the number of adders, the replacement of parallel adaptors by series adaptors and vice versa, possibilities for combining ideal transformers with adaptors without requiring inverse multipliers, and the realization of adaptors with arbitrary numbers of ports by means of elementary adaptors.

Alfred Fettweis

Papers

Wave digital filters: Theory and practice

Wave digital lattice filters

Pseudo-passivity, sensitivity, and stability of wave digital filters

Suppression of parasitic oscillations in wave digital filters

On adaptors for wave digital filters