Novel Approaches to the Design of One Dimensional and Multidimensional Two Channel Filter Banks
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| Publicado en: | PQDT - Global (2009) |
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ProQuest Dissertations & Theses
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| Acceso en línea: | Citation/Abstract Full Text - PDF |
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| Resumen: | Wavelets and filter banks have been widely used in multirate signal processing. Typical applications of filter banks include data compression, image analysis and digital communication. The main focus in filter bank theory and practice is to design critically sampled filter banks with some desirable properties such as frequency selectivity, regularity, symmetry. The problem of designing filter banks with these properties poses an interesting problem and has hence received a lot of attention over many years. In this thesis, we focus on the design of two channel one dimensional and multidimensional filter banks. We present some novel approaches to design them.Conventional filter bank design revolves around “orthogonal” and “biorthogonal” filter banks. There exist different design techniques for these two types of filter banks. Although, both these types have their respective advantages, the biorthogonal type is preferred in image processing applications primarily because the associated filters provide linear phase which is desirable in these applications. In the case of one dimensional two channel filter banks, most of the known biorthogonal filter banks are designed by the factorization of a half band polynomial which has a maximum number of zeros at ω = π or z = −1. However, this method imposes a constraint on every coefficient of the half band filter and hence has no “degree of freedom” that can be utilized. In other words, there is no explicit control over the frequency response of the filters. To address this issue, we start with a general half band filter whose coefficients are parameters to be designed. We then impose the regularity constraint by imposing zeros at the aliasing frequency ω = π. The number of zeros we impose is less than the maximum possible which, therefore, sets aside some free parameters. We use these free parameters to control the frequency response of the filters.The general conditions that must be satisfied by the filters in a filter banks are the perfect reconstruction and alias cancelation conditions. It must be noted that the very nature of these conditions is linear. Therefore, the problem of designing complementary filters is in fact a problem of designing a filter with some linear constraints on its coefficients. These two aspects suggest that it should be possible to design complementary filters using a design approach such as the eigenfilter method. The motivation for this line of thought stems from the fact that the eigenfilter approach to designing FIR filters precisely addresses this issue, wherein it is required to incorporate general linear constraints in the design of the filter. In this thesis, we pursue this line of thought and show how the filter bank design problem can be cast into the framework of the eigenfilter design methodology. The advantage of this method is that it can be applied to the design of one dimensional and multidimensional filter banks.The practical and computationally efficient implementation of filter banks is an interesting problem and has been well researched in the literature, especially for the one dimensional case. Typically, this issue is addressed using “lifting” structures which, by their very construction, are very efficient structures since only the required number of computations are performed in the filtering operation. However, the extension of lifting structures for two dimensional filter banks has been relatively less studied. This extension is not trivial because of the various symmetries that are possible in two dimensional filters and two dimensional signals in general. We address this issue for the design of two dimensional Quincunx filter banks. Particularly, we investigate the conditions that must be satisfied by the predict/update steps of a lifting structure in order for the resultant filters to have quadrantal/diagonal symmetry. |
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| ISBN: | 9798516959899 |
| Fuente: | ProQuest Dissertations & Theses Global |