Stuart Lawson

Design of cascaded allpass structures with magnitude and delay constraints using simulated annealing and quasi-Newton methods

For high sampling rate applications it is useful if the digital filter structure is efficient in the sense of a minimum number of arithmetic operations for a given order. In addition, requirements for satisfying the stringent magnitude and delay specifications lead to the choice of non-minimum phase transfer functions. To this end, a filter structure is considered which is made up from all-pass sections. Two design approaches are examined using classical optimization and simulated annealing. Design examples are provided which illustrate the efficacy of these techniques.<<ETX>>

The design of wave digital filters using fully pipelined bit-level systolic arrays

Wave digital filters (WDF) based on analogue lattice and unit element cascade networks possess important properties that make them suitable for VLSI integration. These include low round-off noise even with short coefficient wordlength and a building block (two-port adaptor) with a very simple structure. Exploiting these properties leads to area efficient designs. Systolic architectures for these WDF networks give the additional advantage of very high sampling rates with potential application in sonar and video signal processing. The bit-level systolic array design of two WDFs is considered in detail, beginning at the filter specification and ending at the VLSI hardware architecture, with discussion of the expected values of the integrated circuit parameters.

On design techniques for approximately linear phase recursive digital filters

Digital filters made from a parallel combination of two allpass branches have been of considerable interest for more than a decade. The design of such filters can be viewed as a phase approximation problem. In this contribution, the behaviour of such filters is examined and several new design techniques are proposed which exploit the known relationships for the magnitude, phase and group delay. The motivation for this study is to explore these relationships more closely with a view to determining the link between various parameters such as filter order, passband and group delay ripple and stopband attenuation. An example is given which illustrates one of the design approaches taken.

Initial and boundary conditions in multidimensional wave digital filter algorithms for plate vibration

Recently, multidimensional wave digital filter (MDWDF) structures have been proposed for the modeling of plate vibration problems. In this paper, we discuss how initial and boundary conditions may be properly embedded into such an algorithm in terms of the state quantities that are an integral part of the algorithm. Due to the essential feature of fully-local interconnectivity in the MDWDF model, different types of boundary conditions can be easily satisfied in a very simple and efficient manner. Instead of remodifying the whole algorithm, usually required by finite elements based methods, boundary conditions in terms of state outputs are simply attached to the model. This feature is especially useful when dealing with the mixed-edges boundary conditions frequently encountered in practice. Graphical results obtained from implementing the MDWDF algorithm are given to further demonstrate the capacities of the method in efficiently handling a fourth-order Mindlin plate vibration system with various types of boundary conditions.

VLSI implementation of wave digital filters using systolic arrays

The authors previously investigated (in Systolic Array Processors, Prentice-Hall, 1989) the application of bit-level systolic arrays to the implementation of wave digital filters developed from cascades of unit elements. The method employed makes use of the characteristic short coefficient word-length property of wave digital filters. Here, they extend it to the case of the lattice wave digital filter (LTWDF). A practical filter design example is considered where a specification is met with 6-b coefficients, and a hardware model is developed for its implementation. Using transistor counts for area estimates, a VLSI floorplan is constructed and probable performance parameters are obtained. The authors find that the techniques are likely to yield area efficient devices capable of performing useful filtering operations at video signal frequencies.<<ETX>>

A general design of mixed IIR-FIR two channel QMF bank

A general family of mixed IIR/FIR two-channel QMF filter banks with near perfect reconstruction (NPR) is presented. The design method is general in the sense that all possible distortions (aliasing, imaging, amplitude and phase distorsions) can be simultaneously and arbitrarily minimized. The method is based on a simple algorithm, also included, to approximate unstable all-pole filters with FIR filters. The resulting filter bank is efficient because a polyphase implementation is possible and delay is low compared to conventional FIR filter banks. It is also shown that some well-known two-channel FIR and IIR filter banks are particular classes of the proposed one. Examples are also included.

The design of 2-D approximately linear phase filters using a direct approach

Abstract A novel approach to the design of approximately linear phase recursive digital filters was recently described. The technique exploited a property of allpass transfer functions which allowed the creation of a set of linear simultaneous equations in the filter coefficients which could then be solved in the least-squares sense. This paper extends the design method to 2-D and multi-D filters. These filters find application in many areas including image processing, image coding, filter banks and seismic data processing. Several problems arise which are not present in the 1-D design and the paper looks at ways to overcome them. In addition, there is discussion on the stability issue. Several examples including circularly, elliptically and diamond symmetric lowpass filters and a fan filter are presented. Comparison is made between the proposed technique and those of Gu and Swamy (1994) and Toyoshima et al. (1990).

Full parallel process for multidimensional wave digital filtering via multidimensional retiming technique

As an alternative approach to the numerical integration of PDEs representing physical systems, the MD-WDF techniques has become of importance due to its attractive features such as massive parallelism and high accuracy inherent in nature. Speed-up efficiencies in terms of achieving fully parallel computing were studied for a 2D-WDF model of the linear transmission line using the chained MD retiming technique. To further explore parallel processing in MD-WDF models using the same pipelining technique, this paper presents the full parallelism for a 3D-WDF model of the linearised shallow water equations (SWEs), which is important in fluid dynamics. Experimental results show that the 3D-WDF model can achieve its full parallelism provided that at most seven parallel processors are each able to implement one multiplication and one addition on one time unit. These results can be extended to nonlinear SWEs, which encounters huge amount of data handling and specific nonlinear optimization problems arising from system modelling.

Multidimensional wave digital filtering approach for numerical integration of non-linear shallow water equations

An alternative approach based on principles of multidimensional (MD) digital signal processing is presented for the solution of a nonlinear physical system. In essence, it consists in the modelling of a continuous (time-dependent) shallow water system by an equivalent discrete passive dynamical system, i.e. system described by difference equations instead of differential equations having the same behaviour as the original one. Details for arriving at the desired discrete system represented by a MD-WDF model are described. In addition, the nonlinearity of the original PDEs is transformed into a system of nonlinear algebraic equations which can be solved without major difficulty by a least-squares method. Graphical results are given to illustrate physical effects of nonlinear water wave propagation including radiation, reflection, refraction, and crest lines from and across the hard boundaries.

Incorporating initial and boundary conditions into the multidimensional wave digital filter

The application of the MD wave digital filter approach to 3D sound propagation described by partial differential equations for acoustic pressure and acoustic fluid velocity is presented. This gives not only a descriptive representation of the physical system, but also a lead to a special kind of discrete realization with advantageous properties. Special attention is paid to the incorporation of properly imposed initial and boundary conditions that are important in practice. Graphical results obtained from the wave digital simulation of sound propagation in two interconnected rooms of a building are given that demonstrates the capabilities of the method.