A Unifying Framework for Finite Wordlength Realizations.

A general framework for the analysis of the finite wordlength (FWL) effects of linear time-invariant digital filter implementations is proposed. By means of a special implicit system description, all realization forms can be described. An algebraic characterization of the equivalent classes is provided, which enables a search for realizations that minimize the FWL effects to be made. Two suitable FWL coefficient sensitivity measures are proposed for use within the framework, these being a transfer function sensitivity measure and a pole sensitivity measure. An illustrative example is presented

The digital implementation of control compensators : the coefficient wordlength issue

Bibliography: leaves 32-34."October, 1979."NASA Ames Grant NGL-22-009-124by Paul Moroney, Alan S. Willsky, Paul K. Houpt

Design and Implementation of Novel FPGA Based Time-Interleaved Variable Centre-Frequency Digital Sigma-Delta Modulators

Novel, multi-path, time-interleaved digital sigma-delta modulators that can operate at any arbitrary frequency from DC to Nyquist are designed, analysed and synthesized in this study. Dual- and quadruple-path fourth-order Butterworth, Chebyshev, Inverse Chebyshev and Elliptical based digital sigma-delta modulators, which offer designers the flexibility of specifying the centre-frequency, pass-band/stop-band attenuation as well as the signal bandwidth are presented. These topologies are compared in terms of their signal-to-noise ratios, hardware complexity, stability, tonality and sensitivity to non-idealities. Detailed simulations performed at the behavioural-level in MATLAB are compared with the experimental results of the FPGA implementation of the designed modulators. The signal-to-noise ratios between the simulated and empirical results are shown to be different by not more than 3-5 dBs. Furthermore, this paper presents the mathematical modelling and evaluation of the tones caused by the finite wordlengths of these digital multi-path sigma-delta modulators when excited by sinusoidal input signals

Quantization effects in the polyphase N-path IIR structure

Polyphase IIR structures have recently proven themselves very attractive for very high performance filters that can be designed using very few coefficients. This, combined with their low sensitivity to coefficient quantization in comparison to standard FIR and IIR structures, makes them very applicable for very fast filtering when implemented in fixed-point arithmetic. However, although the mathematical description is very simple, there exist a number of ways to implement such filters. In this paper, we take four of these different implementation structures, analyze the rounding noise originating from the limited arithmetic wordlength of the mathematical operators, and check the internal data growth within the structure. These analyses need to be done to ensure that the performance of the implementation matches the performance of the theoretical design. The theoretical approach that we present has been proven by the results of the fixed-point simulation done in Simulink and verified by an equivalent bit-true implementation in VHDL

Investigation into digital audio equaliser systems and the effects of arithmetic and transform errors on performance

Merged with duplicate record 10026.1/2685 on 07.20.2017 by CS (TIS)Discrete-time audio equalisers introduce a variety of undesirable artefacts into audio mixing systems, namely, distortions caused by finite wordlength constraints, frequency response distortion due to coefficient calculation and signal disturbances that arise from real-time coefficient update. An understanding of these artefacts is important in the design of computationally affordable, good quality equalisers. A detailed investigation into these artefacts using various forms of arithmetic, filter frequency response, input excitation and sampling frequencies is described in this thesis. Novel coefficient calculation techniques, based on the matched z-transform (MZT) were developed to minimise filter response distortion and computation for on-line implementation. It was found that MZT-based filter responses can approximate more closely to s-plane filters, than BZTbased filters, with an affordable increase in computation load. Frequency response distortions and prewarping/correction schemes at higher sampling frequencies (96 and 192 kHz) were also assessed. An environment for emulating fractional quantisation in fixed and floating point arithmetic was developed. Various key filter topologies were emulated in fixed and floating point arithmetic using various input stimuli and frequency responses. The work provides detailed objective information and an understanding of the behaviour of key topologies in fixed and floating point arithmetic and the effects of input excitation and sampling frequency. Signal disturbance behaviour in key filter topologies during coefficient update was investigated through the implementation of various coefficient update scenarios. Input stimuli and specific frequency response changes that produce worst-case disturbances were identified, providing an analytical understanding of disturbance behaviour in various topologies. Existing parameter and coefficient interpolation algorithms were implemented and assessed under fihite wordlength arithmetic. The disturbance behaviour of various topologies at higher sampling frequencies was examined. The work contributes to the understanding of artefacts in audio equaliser implementation. The study of artefacts at the sampling frequencies of 48,96 and 192 kHz has implications in the assessment of equaliser performance at higher sampling frequencies.Allen & Heath Limite

NATURAL ALGORITHMS IN DIGITAL FILTER DESIGN

Digital filters are an important part of Digital Signal Processing (DSP), which plays vital roles within the modern world, but their design is a complex task requiring a great deal of specialised knowledge. An analysis of this design process is presented, which identifies opportunities for the application of optimisation. The Genetic Algorithm (GA) and Simulated Annealing are problem-independent and increasingly popular optimisation techniques. They do not require detailed prior knowledge of the nature of a problem, and are unaffected by a discontinuous search space, unlike traditional methods such as calculus and hill-climbing. Potential applications of these techniques to the filter design process are discussed, and presented with practical results. Investigations into the design of Frequency Sampling (FS) Finite Impulse Response (FIR) filters using a hybrid GA/hill-climber proved especially successful, improving on published results. An analysis of the search space for FS filters provided useful information on the performance of the optimisation technique. The ability of the GA to trade off a filter's performance with respect to several design criteria simultaneously, without intervention by the designer, is also investigated. Methods of simplifying the design process by using this technique are presented, together with an analysis of the difficulty of the non-linear FIR filter design problem from a GA perspective. This gave an insight into the fundamental nature of the optimisation problem, and also suggested future improvements. The results gained from these investigations allowed the framework for a potential 'intelligent' filter design system to be proposed, in which embedded expert knowledge, Artificial Intelligence techniques and traditional design methods work together. This could deliver a single tool capable of designing a wide range of filters with minimal human intervention, and of proposing solutions to incomplete problems. It could also provide the basis for the development of tools for other areas of DSP system design

A novel approach to the design of DSP systems using minimum complexity Finite State Machines

The paper presents a new and different approach to the design and realisation of Digital Signal Processing (DSP)systems by utilising Finite State Machines (FSM). The DSP system is modelled by mapping all its potential states into an FSM, whose complexity is usually very high. The FSM mirrors the complete functionality of the system and thus describes its behaviour in full detail. Examples for FSMs of first and second order digital recursive filters are provided and the current version of the software simulating the FSM corresponding to any linear time-invariant DSP system is described. The potential of this approach including state reduction techniques as well as the inclusion of non-linear DSP systems is also outlined, and further future research intentions are briefly explored