Class Of Wave Digital Filters Research Articles

Biparametric Wave Digital Filters

We propose a novel class of wave digital filters (WDFs), called Biparametric WDFs (BWDFs), whose power-normalized waves are defined as having two free parameters instead of just one. We explore the advantages brought by this generalization by first deriving the scattering relations and the corresponding adaptation conditions for the most common circuit elements. We then show that the added free parameters allow us to define adaptors whose ports can all be simultaneously adapted; and that these adaptors are reciprocal and their scattering relations can be defined to be multiplierless and independent of the circuit parameters. We also show that the computational cost and memory requirements of BWDFs turn out to be reduced with respect to traditional WDFs based on power-normalized waves. We then discuss the impact of this generalization on the ability of wave digital structures of this sort to accommodate nonlinear elements. We finally develop explicit wave mappings for nonlinear diodes, and discuss some examples of applications to specific nonlinear circuits (i.e., an envelope detector, an unbiased double diode clipper, and a biased double diode clipper).

Synthesis and realization of generalized Chebyshev digital filters with minimum number of multipliers

A synthesis procedure is presented for a class of wave digital filters designed with a minimum number of multipliers. The minimization is achieved by digitizing an appropriate reference analogue symmetrical ladder network having excellent characteristics. The network satisfies an odd-degree generalized Chebyshev response, having an even multiple of transmission zeros at a finite real frequency and the remainder at infinity. Each LC parallel/series resonant branch in the structure is treated as a four-port network and transformed into the appropriate wave digital adaptor with only one multiplier. Synthesizing the digital filter from both ends toward the middle results in a homogeneous structure with a reduced signal path and lowest overall number of multipliers.

Realization of multidimensional GIC digital filters

A realization method for multidimensional Nth-order infinite-impulse-response (IIR) digital filters is proposed. A systematic procedure is presented for synthesizing analog reference networks comprising generalized immittance converters, and resistors, which realize M-variable Nth-order transfer functions. Digital-filter structures are then derived from these reference networks using the wave characterization. The proposed structures are canonic with respect to the number of multipliers and constitute a new class of multidimensional wave digital filters, distinct from the class of wave digital filters derived from doubly terminated LC networks. The realization method is general and relatively simple to apply, and leads to some interesting structures including structures with multiple outputs. >

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.

The analytical transfer functions of wave-digital filters derived from LC ladder prototypes

Based on the wave-chain matrix technique, the paper presents some computationally efficient algorithms for obtaining the polynomial coefficients of the various analytical transfer functions of a class of wave-digital filters derived from the resistance-terminated lossless LC ladder networks, given all the multiplier coefficients. It also describes the numerical methods for computing the multiplier coefficients from the component values of the associated reference filters. The applications of the algorithms in the studies of wave-digital filters are briefly discussed.

Transfer functions of wave-digital filters

The letter presents a numerical algorithm for computing the polynomial coefficients of the transfer functions of a class of wave-digital filters derived from all-pole reference filters, given the multiplier coefficients.

On the sensitivity of a class of wave digital filters

The first-order sensitivity of Fettweis' wave digital filter is expressed in terms of those of its reference filter from which the wave digital filter is derived. With this explicit relation the numerically observed properties of the wave digital filter sensitivity are explained and the relation itself can be used as an efficient computing method when the sensitivities of the reference filter are available. In obtaining the above mentioned relation, the summed sensitivity invariants are used. We show that such invariants can be obtained as a consequence of impedance scaling and frequency scaling property of the reference filter.

Class of wave digital filters consisting only of adders and multipliers

In the letter, a class of wave digital filters is indicated which can be realised without using any subtraction operation. This simplifies the hardware circuit to be constructed.