Motivated by gas dynamics, we consider the heat diffusion equation which in its standard form allows propagation at an infinite speed, and is thus unphysical. Driven by phenomenological considerations rooted in analogies with RC-transmission lines, we introduce a modified 3D heat equation for an isotropic medium that admits MD internally passive circuit realization using resistances, nonlinear inductances, and capacitances of the type previously introduced elsewhere, which via standard techniques can be transformed into well-known Wave Digital networks in the discrete MD domain.

Wave-digital principles, originally developed for one-dimensional filtering purposes, have later been extended to multidimensional filtering applications and have been shown to be applicable also to numerical integration of physically relevant ordinary and partial (thus multidimensional) differential equations of linear and nonlinear type. They are based on physical concepts such as Kirchhoff circuits, wave quantities, energy and power, passivity etc. They offer a number of advantages such as good stability and, more generally, high robustness (ensured by the availability of a suitable Liapunov function), and proper interpretability in the spectral domain. To these can be added in the multidimensional case, especially for numerical integration of partial differential equations, massive parallelism, full locality, and ease to take into account space- and time-varying parameters and arbitrary boundary shapes and conditions. In the present paper, a brief survey of the method is offered for the multidimensional case.>

This paper shows how to solve a system of plasma equations consisting of Euler's and Maxwell's equation systems by using technique of wave digital filters. Since, in plasmas, the electromagnetic effect superposed in addition to the effect of thermal motion in the fluid, both Kirchhoff circuits derived from the equation systems have to be connected each other, which are transformed into well-known WDF algorithm, leading to a solution of plasma equations.>

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.

CAD tools to support a top-down custom design methodology for integrated digital filters are presented. The methodology is based on a tool-box concept, which makes use of specialised analysis, synthesis and optimization programs at each design level: the network, the architecture and the circuit layout. In this paper, CAD tools for filter synthesis, network optimization and architecture optimization are developed. These tools complement design aids for architecture synthesis, and automatic layout generation (silicon compilers) to create a complete design environment. By combining both synthesis as well as optimization aids at each design level, it is possible to achieve complete automation while retaining efficient use of silicon area, speed and power consumption. Application of these tools to the custom integration of wave digital filters with bit-serial architectures is demonstrated.

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.

Since more advanced transmultiplexer concepts have to compete with elementary alternative solutions derived from simple back-to-back connections, they have to aim at high efficiency and robust performance, the latter meaning that they should be quite insensitive against disturbances inherent to the type of technology adopted. Three solutions satisfying these requirements are reviewed, one for a more conventional technology, one for digital technology, and one for switched-capacitor technology. The first one of these is based on the use of efficient conversion circuits operating primarily in the continuous-time analog domain and the second one on a multistep single-path multiplier-free conversion scheme of a type which is particularly suitable for employing wave digital filters, including branching filters of that type. The third one makes use of an alternative of the second one which does not involve branching filters.