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 new implementation of an IIR digital filter transfer function is presented that is structurally passive and, hence, has extremely low pass-band sensitivity. The structure is based on a simple parallel interconnection of two all-pass sections, with each section implemented in a structurally lossless manner. The structure shares a number of properties in common with wave lattice digital filters. Computer simulation results verifying the low-sensitivity feature are included, along with results on roundoff noise/dynamic range interaction. A large number of alternatives is available for the implementation of the all-pass sections, giving rise to the well-known wave lattice digital filters as a specific instance of the implementation.

/pdf/a-new-approach-to-the-realization-of-low-sensitivity-iir-orb97ntu5d.pdf

A new approach to the realization of low-sensitivity IIR digital filters

It is shown that a large class of real-coefficient doubly-complementary IIR transfer function pairs can be implemented by means of a single complex allpass filter. For a real input sequence, the real part of the output sequence corresponds to the output of one of the transfer functions G(z) (for example, lowpass), whereas the imaginary part of the output sequence corresponds to its "complementary" filter H(z) (for example, highpass). The resulting implementation is structurally lossless, and hence the implementations of G(z) and H(z) have very low passband sensitivity. Numerical design examples are included, and a typical numerical example shows that the new implementation with 4 bits per multiplier is considerably better than a direct form implementation with 9 bits per multiplier. Multirate filter bank applications (quadrature mirror filtering) are outlined.

/pdf/design-of-doubly-complementary-iir-digital-filters-using-a-587br3hc7c.pdf

Design of doubly-complementary IIR digital filters using a single complex allpass filter, with multirate applications

The concepts of losslessness and maximum available power are basic to the low-sensitivity properties of doubly terminated lossless networks of the continuous-time domain. Based on similar concepts, we develop a new theory for low-sensitivity discrete-time filter structures. The mathematical setup for the development is the bounded-real property of transfer functions and matrices. Starting from this property, we derive procedures for the synthesis of any stable digital filter transfer function by means of a low-sensitivity structure. Most of the structures generated by this approach are interconnections of a basic building block called digital "two-pair," and each two-pair is characterized by a lossless bounded-real (LBR) transfer matrix. The theory and synthesis procedures also cover special cases such as wave digital filters, which are derived from continuous-time networks, and digital lattice structures, which are closely related to unit elements of distributed network theory.

/pdf/low-passband-sensitivity-digital-filters-a-generalized-3rqva7ti5o.pdf

Low passband sensitivity digital filters: A generalized viewpoint and synthesis procedures

The class of two-dimensional (2-D) digital transfer functions which possess quadrantal symmetry in their frequency responses is derived. Application of this class in the design of 2-D recursive digital filters is indicated.

https://ieeexplore.ieee.org/iel5/31/23481/01084486.pdf

Quadrantal symmetry associated with two-dimensional digital transfer functions

This paper proposes a new wave digital filter derived from doubly terminated LC-ladder networks by replacing each series or shunt arm element of the ladder by its equivalent digital two-port. It is shown that such two-ports may be cascaded without the use of adapters defined by Fettweis ( 1 ). A number of realizations of the wave digital two-ports, which are canonic with respect to both multipliers and delays, have been obtained. Also a realization which is canonic with respect to multipliers only is given and an example considered using this realization. The sensitivity of this filter with respect to the multiplier coefficient changes due to finite word length is compared with the conventional cascaded digital filter and also the one proposed by Renner and Gupta. It is found that the proposed filter appears to be a more desirable form of implementation than the conventional cascade form and comparable to that of Renner and Gupta ( 2 ).

A new type of wave digital filter

This paper proposes a method of obtaining a two-dimensional wave digital filter of the recursive type from a doubly terminated LC-ladder network in two variables by replacing each series or shunt arm element of the ladder by its equivalent digital two-port. A number of realizations of the wave digital two-ports, which are canonic in multipliers, have been obtained. An example of a circularly symmetric low-pass two-dimensional digital filter is considered using these realizations. The sensitivity of this filter with respect to the multiplier coefficient changes due to finite word length is compared with that of the direct realization. It is found that the wave digital filter appears to be a more desirable form of implementation than the conventional cascade form.

K.S. Thyagarajan

Papers

A new type of wave digital filter

Two-dimensional wave digital filters using doubly terminated two-variable LC-ladder configurations