Local orthogonal bases I: Construction

Bernardini, R.; Kovačević, Jelena

doi:10.1007/bf01826247

Cited by 19 publications

(23 citation statements)

References 10 publications

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“…The conditions that group F, weights s(u) and window w must satisfy in order to obtain an orthogonal decomposition of 12x are presented in the first part of this work [1], where the reader can also find all the details pertaining to notation. It is worth remembering, as a result from the first part, that window w must satisfy the condition of power-complementarity:…”

Section: Introductionmentioning

confidence: 99%

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Local orthogonal bases II: Window design

Bernardini

Kovačević²

1996

Multidim Syst Sign Process

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Abstract. In the first part of this work we presented a technique to find a local orthogonal basis for a given vector space. The concept of a local orthogonal basis can be seen as an extension of the one-dimensional local cosine basis used, for example, in audio processing. Here the problem of window design is discussed, with a particular emphasis on the two-dimensional case, both in continuous and discrete time.

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Section: Introductionmentioning

confidence: 99%

“…In the first part of this work [1] we presented a general theory for the construction of local orthogonal bases. The scenario is the following: we have a set X and a vector space l)x of functions defined on X and we want to find a basis bi,j, i, j = 1, 2 .…”

Section: Introductionmentioning

confidence: 99%

Local orthogonal bases II: Window design

Bernardini

Kovačević²

1996

Multidim Syst Sign Process

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“…Other papers that mention or pursue some representationtheoretic aspects of multiresolution analysis include [3], [6], [8], [9], [11], [12], [13], [21], [22], [26], [27], but these complement rather than overlap substantially with this paper. The work of Chirikjian and his collaborators, [5], [15], uses the tools of harmonic analysis on the affine group and motion groups in various pattern recognition problems.…”

Section: Introductionmentioning

confidence: 99%

An algebraic approach to multiresolution analysis

Foote

2005

Trans. Amer. Math. Soc.

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Abstract. The notion of a weak multiresolution analysis is defined over an arbitrary field in terms of cyclic modules for a certain affine group ring. In this setting the basic properties of weak multiresolution analyses are established, including characterizations of their submodules and quotient modules, the existence and uniqueness of reduced scaling equations, and the existence of wavelet bases. These results yield some standard facts on classical multiresolution analyses over the reals as special cases, but provide a different perspective by not relying on orthogonality or topology. Connections with other areas of algebra and possible further directions are mentioned.

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“…In [17], we extend the theory of local cosine bases (cosine-modulated filter banks) to a more general case. In a cosine-modulated filter bank, all the filters are obtained by modulating a prototype filter (also known as the window) with suitable cosine functions.…”

Section: Summary Of Local Orthogonal Basesmentioning

confidence: 99%

“…Consider the one-dimensional (1-D) case as an example. From [17], we can deduce a recipe to obtain a critically sampled orthogonal filter bank with filters of length .…”

Section: Summary Of Local Orthogonal Basesmentioning

confidence: 99%

Arbitrary tilings of the time-frequency plane using local bases

Bernardini

Kovačević

Proceedings of Data Compression Conference - DCC '96

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Abstract-We show how to design filters given a prescribed tiling of the time-frequency plane. Moreover, we impose on these filters the structure of local orthogonal bases. These bases were recently constructed as a generalization of the cosinemodulated filter banks in discrete time and local trigonometric bases in continuous time. They have been found to be of considerable practical importance due to their simplicity (all filters are obtained from a single prototype) and low computational complexity. We show examples of design, in particular, that of a critical-band system for use in audio coding.

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Local orthogonal bases I: Construction

Cited by 19 publications

References 10 publications

Local orthogonal bases II: Window design

Local orthogonal bases II: Window design

An algebraic approach to multiresolution analysis

Arbitrary tilings of the time-frequency plane using local bases

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