Persistent Link:
http://hdl.handle.net/10150/289984
Title:
Filter-bank transforms with exact inverses
Author:
Parra, Paulo Mario
Issue Date:
2003
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Uniformly sampled filter-bank transforms and their inverses are introduced and the conditions to obtain perfect reconstruction upon inversion are explored. It is shown that perfect reconstruction requires both filter addition and multiplication and the necessary and sufficient conditions for these operations are given. Examples indicate how to use the conditions to construct perfect-reconstruction synthesis filters from a given set of analysis filters. Additionally, an iterative scheme is presented that achieves exact inversion to an arbitrary accuracy. The methods to obtain synthesis filters are applied to discretizations of the continuous wavelet transform using both finite and infinite impulse response filters. If exact reconstruction is not a requisite, it is possible to improve imperfect-reconstruction filter banks so that their inverse is closer to the input signal. Two methods to achieve such improvement are described. To better understand the discretizations, one has to look at the continuous case. Therefore the discrete-time filter-bank transforms definitions are extended to continuous-time signal processing. It is shown that the Gabor and continuous wavelet transforms are special cases of the continuous-time extension. The methods introduced in the discrete-time case are used to derive all the linear time-invariant synthesis functions of these two transforms. A straightforward generalization of the Gabor and wavelet transforms generates filter banks whose bandwidths can vary arbitrarily with center frequency. These filters are used to create a cochlear transform, i.e., a "mixed" transform that behaves like a Gabor transform at low center frequencies and like a continuous wavelet transform at high center frequencies. The methodology described in this thesis is implemented in a set of algorithms whose complete documentation are given in chapter 4.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Applied Mechanics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Marcellin, Michael

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleFilter-bank transforms with exact inversesen_US
dc.creatorParra, Paulo Marioen_US
dc.contributor.authorParra, Paulo Marioen_US
dc.date.issued2003en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractUniformly sampled filter-bank transforms and their inverses are introduced and the conditions to obtain perfect reconstruction upon inversion are explored. It is shown that perfect reconstruction requires both filter addition and multiplication and the necessary and sufficient conditions for these operations are given. Examples indicate how to use the conditions to construct perfect-reconstruction synthesis filters from a given set of analysis filters. Additionally, an iterative scheme is presented that achieves exact inversion to an arbitrary accuracy. The methods to obtain synthesis filters are applied to discretizations of the continuous wavelet transform using both finite and infinite impulse response filters. If exact reconstruction is not a requisite, it is possible to improve imperfect-reconstruction filter banks so that their inverse is closer to the input signal. Two methods to achieve such improvement are described. To better understand the discretizations, one has to look at the continuous case. Therefore the discrete-time filter-bank transforms definitions are extended to continuous-time signal processing. It is shown that the Gabor and continuous wavelet transforms are special cases of the continuous-time extension. The methods introduced in the discrete-time case are used to derive all the linear time-invariant synthesis functions of these two transforms. A straightforward generalization of the Gabor and wavelet transforms generates filter banks whose bandwidths can vary arbitrarily with center frequency. These filters are used to create a cochlear transform, i.e., a "mixed" transform that behaves like a Gabor transform at low center frequencies and like a continuous wavelet transform at high center frequencies. The methodology described in this thesis is implemented in a set of algorithms whose complete documentation are given in chapter 4.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectApplied Mechanics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorMarcellin, Michaelen_US
dc.identifier.proquest3108941en_US
dc.identifier.bibrecord.b44830270en_US
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