On hilbert space design of least-weighted-squares digital filters

Numerical convolution operations, executed on noise contaminated signals, are approximated by FIR digital filters in such a way that the effect of random coloured noise is minimized. Using elementary Hilbert space techniques, the filter functions of certain least-weighted-squares digital filters are derived explicitly by the use of discrete orthogonal functions (e.g. Hahn polynomials). the approach is suitable especially for narrowband operations such as smoothing, narrowband differentiation, and narrowband deconvolution (resolution enhancement). Examples of linear-phase lowpasses with monotone passband, obtained with the aid of Hahn polynomials, are discussed in detail. Also the well-known maximally flat digital lowpasses which can be derived with the aid of Krawtchouk polynomials, and narrowband differentiators are considered. In the case of least-weighted-squares approximation by Hahn polynomials, powerful recursive realizations can be developed to reduce computational requirements.     

Substructuring of space and time in TLM diffusion applications

A simple method is described for spatial substructuring of meshes used in TLM diffusion routines in such a way as to enable discontinuous mesh lines to be used. A method of operating TLM diffusion routines using different timesteps in different spatial regions is also described. For both aspects, results are compared with those derived using standard TLM techniques.     

The calculation of radar cross-section (RCS) using the TLM method

The calculation of the radar cross-section (RCS) of complex bodies using the symmetrical condensed TLM method is presented. The technique is based on a near-to-far field transformation of the TLM calculated near fields. Several two-dimensional examples are presented which validate the method. The main advantage of utilizing techniques such as TLM for RCS computation lies in the ability to model arbitrary bodies with complex material compositions.     

Modelling dispersive dielectrics in TLM method

The TLM method, being a time domain method, cannot deal directly with frequency dispersive media. A way for modelling such media, for instance, dielectric dispersive ones, is proposed, starting from the causality relationship between field vectors D and E , which is discretized over the same space–time mesh as the three‐dimensional TLM mesh (in our case, with HSCN node). This leads to adding, at each node on the network, three voltage sources (one for each field component), their value depending on the previous instants. The method is validated by computing the reflection (magnitude and phase) coefficient at normal incidence at an air–dielectric interface, for different dispersive behaviours of the dielectrics. Copyright © 2001 John Wiley & Sons, Ltd.     

Application of the TLM method to two-dimensional scattering problems

In this paper the application of the TLM method to electromagnetic scattering problems is investigated. To achieve the full computational benefits of using a time-domain numerical method, pulse excitation can be applied together with Fourier transformation of an output impulse response to yield frequency-domain results over a wide bandwidth. The configuration of the mesh is the same as that used in FD–TD scattering simulations (i.e., separation of the simulation space into total and scattered field regions). To terminate the exterior boundaries of the mesh, absorbing boundary conditions are applied to absorb the outward travelling waves. The effect of the absorbing boundaries on both time- and frequency-domain results is investigated. Frequency-domain scattered far-field patterns are presented for perfectly conducting square and circular cylinders illuminated by an incident plane wave (TM case). Forward and back scattering cross-section results obtained from a single TLM simulation indicate both the accuracy and efficiency of the method for calculating frequency-domain results over a wide bandwidth.     

A method for algebraic analysis of the TLM algorithm

An analogy is described between the TLM algorithm and discrete state-space control theory. The analogy is used to derive the characteristic equations corresponding to parametrized model structures. Characteristic equations corresponding to several widely used node structures are derived by this means and found to be consistent with the observed behaviour of corresponding TLM models. An example is given of the use of the analogy in teh predictive mode.     

The modelling of multiaxial discontinuities in quasi-planar structures with the modified TLM method

The principal features of the modified TLM method such as the asymmetrical condensed node, graded mesh and dispersion characteristics, are briefly presented. Its general application to multiaxial discontinuities in quasi-planar structures is described, and the modelling of bilateral finline T-junctions is demonstrated in particular.     

TLM法及其一维模型的构造方法

详细介绍了传输线模型法建立一维模型的方法及过程 ,指出TLM法具有概念上的优势和计算的稳定性等优点     

Application of orthogonal curvilinear meshes with SSCN nodes to the TLM method

In previous work novel, techniques with general applications were used to define the transmission line parameters within two‐ and three‐dimensional orthogonal curvilinear meshed space. This paper presents a specific application of the technique and demonstrates that considerable savings in computational load can be achieved when our meshing scheme is applied to 3D electromagnetic problems which are described using the TLM symmetrical super condensed (SSCN) node. Results have been validated using two types of resonant cavity. A comparison of dominant modes confirms that the use of orthogonal curvilinear mesh yields closer agreement with analytical results (using fewer nodes) than would be possible with conventional meshing techniques. Copyright © 2005 John Wiley & Sons, Ltd.     

An investigation into time domain Doppler modelling using the TLM numerical method

The effects observed by a moving source and stationary receiver, or conversely stationary source and moving receiver are well known to physicists. The Doppler effect as it is commonly known is recognized as a perceived change in frequency of the incident signal upon the receiver, caused by the motion of either the source or receiver with respect to the stationary component, occurring in both electromagnetic (transverse) and acoustic (longitudinal) waves. This paper will primarily focus on the acoustic Doppler effect in the time domain, simulating a variety of scenarios using transmission line matrix (TLM) modelling in which the effect can be observed, proceeding to compare the accuracy of the various models generated. A new technique to allow arbitrary placement of boundaries of a TLM mesh will also be introduced and analysed allowing accurate placement of the moving walls within the simulation. Copyright © 2007 John Wiley & Sons, Ltd.     

Use of the two-dimensional TLM method in the electromagnetic simulation of thin semiconductor samples

A two-dimensional lossy shunt TLM node is incorporated into a TLM system and adapted to model for the first time the Maxwell field equations in thin semiconductor samples. Both the characteristics of the node and the TLM system itself are fully described. By considering a parallel-plate structure containing a thin GaAs sample, driven by a voltage source, it is shown, with an example, that this TLM technique can simulate the response of non-stationary electromagnetic fields in a semiconductor to applied excitations.     

Development of an induction motor drive phase model based on the TLM method

This paper describes a phase model of an induction motor based on Transmission-Line Modelling technique. Its main advantage compared to the existing TLM d-q model is the possibility of using a small part of the stator self-inductance of each pahase as a link model to connect the motor to external sources and drives. Unlike the d-q model, the phase model does not therefore require any additional components for connection purposes. The application of the phase model is demonstrated by and example representing a traction drive ciruit. Identical simulation results to those obtained from a different study based on a d-q model are derived.     

Huygens' principle in the transmission line matrix method (TLM). Local theory

Huygens' principle (HP) is a well‐known fundamental principle of wave propagation. More generally, it can be understood as representing the principle of action‐by‐proximity (cf. Faraday's field theory etc.) and the superposition of secondary wavelets re‐irradiated at each point of the wavefront (Huygens' construction). These wavelets are isotropic in free space and in isotropic materials. We will show, that HP is realized within the transmission line matrix method (TLM) for scalar fields in free space of any dimension, if one considers only the scattered fields to represent the secondary wavelets. This corrects and generalizes the previous result for the total field in 2D. This property of TLM provides another explanation for its wide range of applicability. Copyright © 2003 John Wiley & Sons, Ltd.     

Accuracy of the frequency‐domain TLM method and its application to microwave circuits

This paper investigates the accuracy and convergence of frequency‐domain (FD) TLM solutions and describes a method to identify non‐physical solutions. The numerical dispersion characteristics of various discretization schemes (‘nodes’) are compared. The occurrence of non‐physical solutions when solving three‐dimensional problems is discussed and a method to identify the non‐physical solutions is described. The accuracy of the FDTLM method is shown to be of second order as long as singularities are absent, whereas it is between first and second order if the computational domain includes field singularities. Copyright © 2002 John Wiley & Sons, Ltd.     

TLM representation of the hyperbolic heat conduction equation

Many heat transfer situations are adequately described by the parabolic thermal diffusion equation. However, in situations in which very rapid heating occurs or in slower heating regimes for particular materials, the hyperbolic heat conduction equation is a better representation. Here, a parameterized nodal structure for transmission line modelling (TLM) representation of hyperbolic heat conduction processes is devised. A TLM model based on the nodal structure is implemented and temperature field predicted by the model are compared with analytical results for the same physical situation. Copyright © 2002 John Wiley & Sons, Ltd.     

TLM treatments of changes of phase

The existing treatment of an instantaneous endothermic change of state is extended to deal both with exothermic effects and with first order Arrhenius changes. These extended treatments are used to model complex changes of phase occurring during the firing of ball clay and china clay, both of which are constitutents of the slip used in the production of vitreous china ware. The adequacy of the treatments is investigated for both clays by comparing a TLM simulation of a DSC (differential scanning calorimetry) experiment with measurements made during the experiment.     

The modelling of EM leakage into advanced composite enclosures using the TLM technique

The TLM technique has been enhanced to allow the accurate modelling of EM diffusion through advanced composite material shells. This is a significant development owing to the rapidly increasing use of conducting composite materials in aerospace vehicle design. The accurate EM modelling of this class of materials is important for correct design of vehicles with regard to electromagnetic compatibility (EMC). Existing 3-D time-domain TLM models a non-perfectly conducting shell using a resistive sheet (or sheets) to simulate the surface. The results from this model are shown to be slightly inaccurate and require lengthy computer solution times. A separate 1-D, frequency-domain transmission-line model has been developed elsewhere to better analyse the diffusion properties of composite materials. The incorporation of the results from this frequency domain code into the 3-D time-domain TLM algorithm is outlined.     

TLM modelling of the diffusion approximation of queuing system

This paper provides an application of the TLM method to any queuing systems that can be approximated as a diffusion process. The TLM node has been extended in order to take into account the variables associated with the diffusion approximation of the queue, which is presented in Harrison, Patel, Performance Modelling of Communication Networks and Computer Architectures, Addison‐Wesley: Reading, MA, 1994. The analytical solution is compared with the TLM numerical results. Copyright © 2001 John Wiley & Sons, Ltd.