Multi-dimensional Filter Banks and Wavelets—A System Theoretic Perspective
✍ Scribed by sankar basu
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 743 KB
- Volume
- 335
- Category
- Article
- ISSN
- 0016-0032
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✦ Synopsis
We review the current status of multi!dimensional _lters bank and wavelet desin from the perspective of sinal and system theory[ The study of wavelets and perfect reconstruction _lter banks are known to have roots in traditional _lter desin techniques[ On the other hand\ the \_eld of multi!dimensional systems and sinal processinhas developed a set of tools intrinsic to itself\ and has attained a certain level of maturity over the last two decades[ We have recently noted a deree of synery between the two \_elds of wavelets and multi!dimensional systems[ This arises from the fact that many ideas crucial to wavelet desin are inherently system theoretic in nature[ While there are many examples of this synery manifested in recent publications\ we provide a ~avor of techniques ermane to this development by considerina few speci\_c problems in detail[ The construction of orthoonal wavelets can be essentially viewed as a circuit and system theoretic problem of desin of enery dissipative "passive# _lters\ the multi!dimensional version of which has very close ties with a classic problem of lumpedÐdistributed passive network synthesis[ Groebner basis techniques\ matrix completion problems over rins of polynomials or rins of stable rational functions\ i[e[\ QuillenÐSuslin "20# type problems are still other examples\ which feature in our discussion in an important manner[ A number of open problems are also cited[ Þ 0887 The Franklin Institute[ Published by Elsevier Science Ltd[