| Research Staff | Dr Robin John Clark |  |
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| Project | Investigation into Digital Audio Equaliser Systems and the Effects of Arithmetic and Transform Error on Performance | ||
| Director of Studies | Professor Emmanuel Ifeachor | ||
| Supervisors | Glenn M. Rogers | ||
| Robin.Clark@Allen-Heath.com |
Research Project
Investigation into digital audio equaliser systems and the effects of arithmetic and transform errors on performance
Abstract
Discrete-time audio equalisers introduce a variety of undesirable artefacts into audio mixing systems, namely, distortions caused by finite word-length 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 BZT-based filters, with an affordable increase in computation load. Frequency response distortions and pre-warping/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 finite word-length 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.
Publications
Filter Morphing—Topologies, Signals and Sampling Rates
Clark, R.J., Ifeachor, E. C. and Rogers, G. M.
113th AES Convention, Oct. 5-8, 2002. Los Angeles, CA, USA.
Preprint 5661
Investigation into Digital Audio Equaliser Systems and the Effects of Arithmetic and Transform Error on Performance
Techniques for generating digital equaliser coefficients
Clark R. J. Ph.D. Thesis, University of Plymouth, April 2001
Department of Communication and Electronic Engineering, Faculty of Technology
In collaboration with, Allen & Heath Limited
R. J. Clark, E. C. Ifeachor, G. M. Rogers, and P. W. J. Van Eetvelt
Journal of the Audio Engineering Society, Volume 48, Number 4, April 2000
Real-time equaliser coefficient realisation with minimised computational load and distortion
The study of arithmetic and word-length requirements for digital audio filtering hardware
Clark, R.J., Ifeachor, E. C. and Rogers, G. M.
101st AES Convention, Nov.8–11, 1996. Los Angeles, CA, USA.
Preprint 4360
Clark, R.J., Ifeachor, E. C. and Rogers, G. M.
99th AES Convention, Oct 6-9, 1995. New York, USA.
Preprint 5484