New results in numerically integrating PDES by the wave digital approach

Fettweis, A.; Seraji, G.A.

doi:10.1109/iscas.1999.777500

Cited by 6 publications

(2 citation statements)

References 12 publications

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“…They are the standard tool for the frequency domain description of onedimensional systems. However, the application of transfer functions models to scalar and vector PDEs is still a topic of active research [1,5,11]. …”

Section: Transfer Function Modelsmentioning

confidence: 99%

Turning Vector Partial Differential Equations into Multidimensional Transfer Function Models

Trautmann¹,

Rabenstein²

2001

Mathematical and Computer Modelling of Dynamical Systems

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Transfer function models for the description of physical systems have recently been introduced. They provide an alternative to the conventional representation by partial differential equations (PDE) and are suitable for computer implementation. This paper presents transfer function modelling for vector PDEs. They arise from the physical analysis of multidimensional systems in terms of potential and¯ux quantities. Expressing the resulting coupled PDEs in vector form facilitates the direct formulation of boundary and interface conditions in their physical context. It is shown how a carefully constructed transformation for the space variable leads to transfer function models for vector PDEs. They are the starting point for the derivation of discrete models by standard methods for one-dimensional systems. The presented functional transformation approach is suitable for a number of technical applications, like electromagnetics, optics, acoustics and heat and mass transfer. Examples are given for the voltage and current distribution on an electrical transmission line and the velocity and force distribution on longitudinal vibrating strings.

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Section: Transfer Function Modelsmentioning

confidence: 99%

Turning Vector Partial Differential Equations into Multidimensional Transfer Function Models

Trautmann¹,

Rabenstein²

2001

Mathematical and Computer Modelling of Dynamical Systems

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“…The theory, principles, and properties of wave digital filters are well explained in variety of publications delivered by several authors [1][2][3][4][5][6][7][8]. Although digital filtering is the principal application of wave digital filters, they have interesting applications in numerical integration and state-space simulation [9,10].…”

Section: Introductionmentioning

confidence: 99%

On the design of multiband transmission functions synthesized by one wave digital lattice structure

Yaseen

2011

Circuit Theory & Apps

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SUMMARYIn this contribution, the design of multiband transmission functions is considered. Independent and arbitrary number of bands can be designed. Moreover, the whole transmission function is synthesized by one wave digital lattice structure. The approximation process starts by extracting the scattering matrix properties of multiband reference lattice structures. Consequently, the approximation problem reduces to generating a polynomial Q of degree n, which is the degree of the filter. The degree n is depending on the number of the designed bands. Hence, if the number of bands is even, n will be odd, and if the number of bands is odd, n will be even. The polynomial Q will approximate the difference phase function of the two branch polynomials. It is composed of two subpolynomials, one of them is Hurwitz and the other is anti-Hurwitz. The degrees of these subpolynomials differ by odd number if the number of bands is even and differ by even number if the number of bands is odd. Q is generated according to iterative interpolation and using explicit recursive formulas. After obtaining Q, the two subpolynomials are calculated and the two branch all-pass functions are constructed. Consequently, the filter is synthesized in the digital frequency domain. The method is applied through an illustrative example.

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Automatic Generation of Wave Digital Structures for Numerically Integrating Linear Symmetric Hyperbolic PDEs

Vollmer

2005

Multidim Syst Sign Process

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New results in numerically integrating PDES by the wave digital approach

Cited by 6 publications

References 12 publications

Turning Vector Partial Differential Equations into Multidimensional Transfer Function Models

Turning Vector Partial Differential Equations into Multidimensional Transfer Function Models

On the design of multiband transmission functions synthesized by one wave digital lattice structure

Automatic Generation of Wave Digital Structures for Numerically Integrating Linear Symmetric Hyperbolic PDEs

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