The University of Southampton
University of Southampton Institutional Repository

Constrained adaptive filtering and application to sound equalisation

Constrained adaptive filtering and application to sound equalisation
Constrained adaptive filtering and application to sound equalisation

In this thesis, a bound is constructed for the value of the convergence coefficient and penalty parameter. This will give conditions for convergence and hence enable more accurate and faster converging adaptive algorithms using the penalty method. The penalty is implemented by using the function {max[ci, 0]}, which is computationally efficient. The theoretical bound on the values for the adaptive LMS and FDLMS algorithms with quadratic constraints is established. The performance is significantly improved by using the new established bound as shown by simulation. In the case of using the second order penalty function max(ci, 0)2, the quadratic constraints can be approximated using linear constraints. Using these linear constraints rather than the original quadratic constraints will mean that the new objective function will be quadratic, so that the new bound defined can also be suitable for the second order penalty function. Simulation showed that using linear constraints with a second order penalty function formulation converged to a minimum that was very close to the quadratically constrained case.  Increasing the convergence rate of the FDLMS algorithm can also be achieved by incorporating the Bin-normalised FDLMS and the conjugate gradient (CG) algorithms. Efficient constrained BN-FDLMS and CG algorithms implemented in the frequency domain are developed and studied. Their performance showed that they have superior convergence rate compared with the constrained FDLMS.

The new constrained adaptive filtering algorithms studied and developed here were applied to the problem of sound equalisation in an enclosed room. It is also shown that spatial robustness can be further improved by using frequency-dependent constraints, by utilizing the structure of the spatial correlation in a reverberant sound field. A simulation study of the frequency-dependent constraints verifies the applicability of the new algorithms.

University of Southampton
Tam, Pik Shan
f221fbb3-cea2-468e-b58d-574fe5221362
Tam, Pik Shan
f221fbb3-cea2-468e-b58d-574fe5221362

Tam, Pik Shan (2003) Constrained adaptive filtering and application to sound equalisation. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

In this thesis, a bound is constructed for the value of the convergence coefficient and penalty parameter. This will give conditions for convergence and hence enable more accurate and faster converging adaptive algorithms using the penalty method. The penalty is implemented by using the function {max[ci, 0]}, which is computationally efficient. The theoretical bound on the values for the adaptive LMS and FDLMS algorithms with quadratic constraints is established. The performance is significantly improved by using the new established bound as shown by simulation. In the case of using the second order penalty function max(ci, 0)2, the quadratic constraints can be approximated using linear constraints. Using these linear constraints rather than the original quadratic constraints will mean that the new objective function will be quadratic, so that the new bound defined can also be suitable for the second order penalty function. Simulation showed that using linear constraints with a second order penalty function formulation converged to a minimum that was very close to the quadratically constrained case.  Increasing the convergence rate of the FDLMS algorithm can also be achieved by incorporating the Bin-normalised FDLMS and the conjugate gradient (CG) algorithms. Efficient constrained BN-FDLMS and CG algorithms implemented in the frequency domain are developed and studied. Their performance showed that they have superior convergence rate compared with the constrained FDLMS.

The new constrained adaptive filtering algorithms studied and developed here were applied to the problem of sound equalisation in an enclosed room. It is also shown that spatial robustness can be further improved by using frequency-dependent constraints, by utilizing the structure of the spatial correlation in a reverberant sound field. A simulation study of the frequency-dependent constraints verifies the applicability of the new algorithms.

Text
928657.pdf - Version of Record
Available under License University of Southampton Thesis Licence.
Download (26MB)

More information

Published date: 2003

Identifiers

Local EPrints ID: 465220
URI: http://eprints.soton.ac.uk/id/eprint/465220
PURE UUID: 8f54284a-965a-4a9a-98f1-b5d05b62777a

Catalogue record

Date deposited: 05 Jul 2022 00:29
Last modified: 16 Mar 2024 20:02

Export record

Contributors

Author: Pik Shan Tam

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×