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

http://ieeexplore.ieee.org/iel6/53/26079/01162225.pdf

The acoustics, speech, and signal processing society - A historical perspective

A framework is presented for the analysis, representation, and evaluation of digital filter structures. Based on the notation of linear signal-flow graphs and their equivalent matrix representation, a set of general linear digital network properties are reviewed, including precedence relations computability, Tellegen's theorem, interreciprocity, and network transposition. These properties are then utilized in developing time and frequency domain analysis techniques and sensitivity analysis techniques. These techniques, in turn, are applied to the comparison of several basic digital filter structures.

/pdf/analysis-of-linear-digital-networks-465v12q5bo.pdf

Analysis of linear digital networks

A class of low-sensitivity digital ladder filters may be realized in the voltage-current domain by direct analogy with the continuous resistively terminated LC ladder filter The problem of unrealizability that is implied by delay-free loops in the discrete signal flow graph is overcome by using transformations that correspond to LC elements that exhibit finite Cube factors The resultant deterioration in the passband of the transfer function is determined from the Blowstein LC ladder sensitivity theory and is, thereby, shown to be low valued at high sampling frequencies The sensitivity properties of this class of digital ladder filters are directly analogous to the LC prototype because each LC element is replaced by a digital multiplier Consequently, if maximum power transfer is approximately maintained throughout the passband of the LC prototype, then the first-order sensitivity of the corresponding digital transfer function to multiply a coefficient quantization is necessarily low valued

Low-sensitivity digital ladder filters

Recently, there has been a great deal of interest in the implementation of digital filter structures with low-coefficient word length. A conjecture has been made by Fettweis that if digital filter structures are modeled after analog ladder structures, which are known to have desirable coefficient sensitivity properties, then the digital ladder structures will also have these properties and could be implemented with low-coefficient word lengths. To investigate this conjecture, a seventh-order Chebyshev low-pass filter was realized as a digital ladder structure and the coefficient sensitivity was analyzed experimentally under coefficient rounding in floating-point representation. To serve as a comparison similar examples of cascade structures of direct and coupled form sections were also analyzed in the same manner. The conclusions drawn are that, indeed, the digital ladder structures in many cases can be implemented with lower coefficient word lengths than the conventional structures.

Digital ladder structures and coefficient sensitivity

A modification is proposed in the design of digital ladder structures, which have transmission zeros. This results in a reduction in the number of adds required in the structure. The location of the transmission zeros under coefficient rounding is then analyzed.

R. Crochiere

Papers

Digital ladder structures and coefficient sensitivity

On the location of zeros and a reduction in the number of adds in a digital ladder structure