Wave Digital Filters Research Articles

Sensitivity of driving-point function based wave digital filters

It is shown that the passband sensitivity advantage with respect to the terminating multipliers claimed for driving-point based wave digital filters does not exist in practice. It is also shown that the performance of these filters is poor compared to that of conventional transfer function based wave digital filters as far as the stopband sensitivity is concerned.

A consideration for the interpolation problem with first‐and second‐order information

AbstractA wave digital filter (WDF) is a low‐sensitivity digital filter which simulates lossless analog circuits. A lattice‐type digital filter (AR lattice filter), which is used in digital signal processing, is a WDF equivalent to a cascade of unit elements (u.e.). As the generalization of this relation, a WDF realizing a modeling filter for an ARMA process has been obtained and the network theory with WDF's has been applied to the digital signal processing. The conventional WDF's, except for the AR lattice filter, are constructed by using the transfer functions to be realized. In this paper, unlike the conventional network synthesis, we propose a synthesis method. In this method, a network approximating a modeling filter for a stationary stochastic process is synthesized recursively using a finite number of data of the autocorrelation coefficients (second‐order information) and the impulse response of the modeling filter (first‐order information). A lattice‐type digital filter is derived realizing an approximation of the transfer function. The approximation is one in which first‐ and second‐order information matches the forementioned data. Also, modified least square approximations due to Kalman and Mullis can be realized by this lattice‐type digital filter. This lattice‐type digital filter is a kind of WDF and the relationship between the global stability and the local stability is clear.

Correction to "Wave digital filters: Theory and practice"

Correction to "Wave digital filters: Theory and practice"

Alternative method to magnitude truncation in wave digital filters

It will be shown how dissipation can be introduced in a class of wave digital filters involving two-port adaptors without necessarily increasing the number of adders and multipliers. The dissipation introduced this way represent an alternative method to magnitude truncation.

Design of two-dimensional pseudorotated digital filters satisfying prescribed specifications

Two methods for the design of two-dimensional (2-D) rotated digital filters proposed by Costa and Venetsanopoulos and Goodman are modified by performing rotation through a somewhat more general transformation. This modification eliminates nonessential singularities of the second kind, which can lead to an unstable 2-D digital filter when finiteprecision arithmetic is used for the implementation. The paper also describes detailed procedures for the design of 2-D rotated digital filters satisfying prescribed specifications. The procedures can be used for the design of low-pass, high-pass, bandpass, and bandstop filters of the Butterworth, Chebyshev, or elliptic type, and also for the design of wave digital filters. The specifications that can be prescribed are the maximum passband ripple, the minimum stopband attenuation, the passband and stopband edges, and the degree of circularity. Further, zero phase can readily be achieved.

Equivalent transformations and sensitivity of wave digital filters

AbstractWave digital filters (WDF's) are well known to have a low‐sensitivity property in general. In addition to several existing design approaches, new circuit realizations of series and parallel sections are proposed in this paper. Also, equivalent transformations are presented which enable new WDF's to be derived from those of Fettweis. Accordingly, many kinds of equivalent WDF's can be designed from a single analog prototype filter. The comparison of sensitivity characteristics of these circuits shows that far less sensitive WDF's can be realized by an appropriate choice from the conventional and the new sections depending on the value of their internal multiplier coefficients.

On Complimentary and sensitivity of generalized wave digital filters

In recent literature, a general theory has been developed to design low-sensitivity digital filter structures in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> -domain. These structures are two-ports with two inputs and two outputs and wave digital filters belong to this general class. This paper explores the significance of the para-unitary or complementary condition on generalized wave digital filters. Satisfying this condition allows, for example, the simultaneous generation of low- and high-pass filter outputs. There is discussion too of sensitivity and its significance to those generalized wave digital filter structures that do not satisfy the para-unitary condition.

Transfer functions for switched-capacitor and wave digital filters

Closed-form expressions are presented for amplitude-oriented low-pass, high-pass, and bandpass sampled-data transfer functions suitable for realization as 1) switched-capacitor lossless discrete integrator (LDI) ladder filters, or 2) wave digital filters. Other types of realizations are also possible, such as those employing voltage inverter switches (VIS's), the recently introduced switched-capacitor "voltage wave" filters, and standard recursive digital realizations. The filters possess optimum equirippie (or maximally flat) passbands and monotonic stopbands with arbitrary selectivity. The low-pass and high-pass cases are derived from distributed passive prototype functions, but the more important bandpass functions are quite novel, appearing here for the first time.

Synthesis of arbitrary digital transfer functions using allpass-based structures derived via LBR two-pair extraction procedure

The implementation of a digital filter transfer function with all transmission zeros on the unit circle is developed via the synthesis of an appropriate allpass function. The synthesis procedure is based on the “LBR-extraction” approach. The resulting structure is in the form of a doubly terminated cascade of lossless (LBR) two-pairs, with each two-pair realizing a single real or a pair of complex transmission zeros. The Concepts of complete and partial “1” removals, and “1” shifting are introduced and utilized during the synthesis process. The resulting structures have several properties in common with the Gray and Markel lattice filters, but do not require tap coefficients for numerator realization. The building blocks used in this paper are similar to those in certain wave-digital filters and orthogonal filters.

Novel realization of hilbert transformer using complex wave digital filters

A complex network can be interpreted as a connection consisting of two real networks, one of which transfers the real part of the complex signal and the other transfers the imaginary part. In this paper, a realization of complex filters using wave digital lattice filters is reported. The relation between the real part and the imaginary part of its output fulfills the Hilbert transformation. As the attenuation response of a wave digital lattice filter meets some symmetrical requirements, a certain amount of hardware can be saved. Explicit formulae and the Hilbert transformer table are given. The disgn process is so simple that a pocket programmable calculator is sufficient to carry out the necessary calculations.

Transfer function realization of a class of doubly-terminated two-variable lossless networks and their application in linear-phase 2-dimensional digital filter design

A method is presented for the design of a class of two-dimensional (2-D) stable digital filters satisfying prescribed magnitude and constant group delay specifications. The design method generates a 2-D digital transfer function which is a product of two transfer functions H 1 ( z 1 , z 2 ) and H 2 ( z 1 , z 2 ), corresponding to a recursive filter and a nonrecursive filter, respectively, Component H 1 ( z 1 , z 2 ) ensures a wave-digital realization, that is, the design method guarantees the generation of a corresponding analog function H 1A ( s 1 , s 2 ) which is realizable as the transfer function of a doubly-terminated two-variable lossless network. Thus the design technique ensures that not only is a given frequency response achieved, but also the generated transfer function is realizable as a cascade of a wave-digital filter and a nonrecursive digital filter. The class of filters considered here is one in which the doubly-terminated analog network used to realize the wave digital filter is a cascade of s 1 - and s 2 -variable lossess two-ports with all their transmission zeros at infinity.

Wave digital filters: Theory and practice

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.

Finite wordlength design of wave digital filters

The letter illustrates some examples from a software package for the design of finite wordlength wave digital filters (WDFs). Given a set of initial coefficients, the program generates a new set of coefficients which are quantised to the required number of bits. Some filter design examples have been considered to illustrate this for three types of WDF, i.e. unit element, lattice and LC-ladder WDFs.

Wave digital filters based on extracting two‐wire lines

AbstractIt is well known that wave digital filters (WDF's) imitating the behavior of doubly terminated reactance circuits have low coefficient sensitivity properties. Based on the Darlington synthesis procedure, a cascade synthesis of WDF's realizing arbitrary transfer functions has been shown. They are constituted with cascading basic WDF sections corresponding to basic reactance sections. The cascade synthesis procedure, however, is rather complicated in that transmission zeros have to be found by calculating the roots of an algebraic equation.

Design of Bireciprocal Wave Digital Filters for High Sampling Rate Applications

Design of Bireciprocal Wave Digital Filters for High Sampling Rate Applications

A hybrid domain articulatory speech synthesizer

Articulatory speech synthesizers model the human vocal tract by means of its geometrical and functional properties. It is believed that this approach can be advantageous in speech coding at bit rates below 4800 b/s. Existing articulatory synthesizers work in the time domain. They either solve a system of differential equations for the vocal tract and the glottis, or synthesize speech using wave digital filters. The first approach is computationally very cumbersome. Both approaches have difficulties in incorporating important acoustic parameters, for example, the radiation impedance at the lips, wall vibration, and other losses. So far a realistic glottis model suitable for the wave digital filter approach does not exist. We have combined a nonlinear time‐domain model of the vocal cords [K. Ishizaka and J. L. Flanagan, Bell Syst. Tech. J. 51, 1233–1268 (1972)] with a linear frequency‐domain chain‐matrix model of the vocal tract [e.g., M. M. Sondhi, paper ♯4.5.1, Proc. Int. Congress on Acoustics, Paris, France, 1983, Vol. 4, pp. 167–170]. The interface between these two models consists of convolving the glottal flow in the time domain with impulse responses of the tract obtained by inverse FFT. Examples of synthesized speech using manually generated and measured tract areas will be given.

Reconstruction of signals after filtering and sampling rate reduction

A wave digital filter (WDF) two-port has two input and two output-terminals. By using these to appropriately connect a WDF to its transpose, the filtering effect is fully compensated except for an all-pass phase, and this independently of any selectivity requirement. This remains true if at the points of interconnection, every second sample is reduced to zero, provided that a certain condition, easily to be satisfied exactly, is fulfilled. Very efficient solutions are then possible. The method is of interest, e.g., for subband coding.

A unified approach to orthogonal digital filters and wave digital filters, based on LBR two-pair extraction

The LBR-extraction approach is extended in order to derive wave digital filters and several orthogonal digital filters in a unified manner. The derivation clearly places in evidence the underlying orthogonality property of all these structures, which can therefore be implemented based on a simple building block, namely, the "planar rotation" operator. The derivation directly emphasizes the concept of "structural boundedness" as a requirement for low sensitivity. In addition to wave and orthogonal filters, a number of other methods for forcing structural boundedness are indicated.

New wave digital filters for basic reactance sections

This paper describes new wave digital, realizations with the canonic number of delays of Brune, type- C , type- E , and type- D sections, which are used as basic sections for the cascade synthesis of general wave digital filters. These basic wave digital filters are derived from the distributed equivalents of basic sections constituted with one or two sections of two-wire lines, and their modified forms which have a reflection-free port are also presented. Although these basic wave digital filters do not have the exact equivalence with basic sections when their multiplier coefficients are quantized, some examples show that the wave digital filters realized with the proposed basic wave digital filters have still good sensitivity properties.

Passivity properties of low-sensitivity digital filter structures

A general representation of a class of low passband sensitivity digital filter structures is proposed. The proposed representation for a transfer function of order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> consists of an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(N + 1)</tex> -pair memoryless system terminated at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -pairs by delays. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(N + 1)</tex> -pair system contains only adders and multipliers, and is described by an orthogonal transfer matrix. The set of terminating delays can be looked upon as an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -pair system with transfer matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z^{-1}{\bf 1}</tex> . Certain wave digital filter structures, Gray-Markel lattice structures and the coupled-form biquadratic section belong to the general form advanced here. Several properties satisfied in these special cases are derived in a unified manner using the generalized representation. Also, a quantization scheme that makes the structure free from zero-input limit cycles even under time-varying conditions is advanced, unifying similar such results independently reported for the above well-known structures.