Turning Vector Partial Differential Equations into Multidimensional Transfer Function Models

Turning Vector Partial Differential Equations into Multidimensional Transfer Function Models

Solution of vector partial differential equations by transfer function models

Transfer function models for the description of physical systems have recently been introduced to the field of multidimensional digital signal processing. They provide an alternative to the conventional representation by partial differential equations (PDE) and are suitable for computer implementation. This paper extends the transfer function approach to vector PDEs. They arise from the physica...

Multidimensional Transfer Function Models

Transfer functions are a standard description of onedimensional linear and time-invariant systems. They provide an alternative to the conventional representation by ordinary differential equations and are suitable for computer implementation. This article extends that concept to multidimensional (MD) systems, normally described by partial differential equations (PDEs). Transfer function modelin...

Transfer Function Models for Multidimensional Systems

Multidimensional systems describe relations between signals depending on two or more independent variables, like time and space. They are also called distributed parameter systems. The only conventional model for their description are partial diierential equations. This is in contrast to onedimensional (lumped parameter) systems, where a variety of diierent models including transfer functions i...

Optimized Difference Schemes for Multidimensional Hyperbolic Partial Differential Equations

In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy) that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may...