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Multidimensional orthogonal filter bank characterization and design using the Cayley transform

Multidimensional orthogonal filter bank characterization and design using the Cayley transform,10.1109/TIP.2005.847323,IEEE Transactions on Image Proc

Multidimensional orthogonal filter bank characterization and design using the Cayley transform   (Citations: 11)
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We present a complete characterization and design of orthogonal infinite impulse response (IIR) and finite impulse response (FIR) filter banks in any dimension using the Cayley transform (CT). Traditional design methods for one-dimensional orthogonal filter banks cannot be extended to higher dimensions directly due to the lack of a multidimensional (MD) spectral factor- ization theorem. In the polyphase domain, orthogonal filter banks are equivalent to paraunitary matrices and lead to solving a set of nonlinear equations. The CT establishes a one-to-one mapping be- tween paraunitary matrices and para-skew-Hermitian matrices. In contrast to the paraunitary condition, the para-skew-Hermitian condition amounts to linear constraints on the matrix entries which are much easier to solve. Based on this characterization, we pro- pose efficient methods to design MD orthogonal filter banks and present new design results for both IIR and FIR cases.
Journal: IEEE Transactions on Image Processing , vol. 14, no. 6, pp. 760-769, 2005
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    • ...We are interested here by orthogonal FBs, for which there are relatively few design methods: [5] employs a lattice parameterization of paraunitary matrices (incomplete in more than one dimension), [6] and [7] are based on direct optimization, initialized with a diamond shaped filter, [8] proposes an iterative fitting with a nonfactorable product filter, and [9] uses the Cayley transform and a nice characterization of paraunitarity...
    • ...The first three methods use nonconvex optimization and [9] reduces the problem to solving systems of quadratic equations...
    • ...Example 2: We compare now with the designs from [9]...
    • ...Comparing with the result from [9], which has the advantage of maximum regularity ,w e see that our design has better phase linearity, but slightly worse orthogonality error...

    Bogdan Dumitrescu. A Moulding Technique for the Design of 2-D Nearly Orthogonal Filter Ba...

    • ...Two-dimensional (2-D) filters and filter banks have been a subject of intensive research due their wide applications in numerous fields (see e.g [4], [8], [9], [14], [16] and references therein)...
    • ...nonseparable filters are unavoidable [5], [7], [8], [10]‐[12], [14]‐[16]...

    T. Q. Hunget al. Design of Diamond and Circular Filters by Semi-definite Programming

    • ...<{[SECTION]}>of intensive research (see e.g. [4, 8, 15] and the references...

    T. Q. Hunget al. SDP for 2-d Filter Design: General Formulation and Dimension Reduction...

    • ...Recently we proposed a complete characterization of MD orthogonal filter banks using the Cayley transform and designed some orthogonal filter banks for both IIR and FIR cases [14]...
    • ...In this subsection, we briefly review the main results on the characterization of paraunitary matrices via the Cayley transform [14] that will be used later in the paper...
    • ...The CT maps a paraunitary matrix to a para-skew-Hermitian (PSH) matrix [14], [17]...
    • ...Theorem 3: ([14]) The Cayley transform of a matrix H(z) is a paraunitary FIR matrix if and only if H(z) can be written as H(z) = H′(z)/D(z), where D(z) is an FIR filter and H′(z) is an FIR matrix, and they satisfy the following four...
    • ...Proposition 4: ([14]) Suppose W(z) is a multidimensional...
    • ...For design details and examples, please see [14]...

    Jianping Zhouet al. Special paraunitary matrices, Cayley transform, and multidimensional o...

    • ...The Cayley transform has been used in the characterization and design of multidimensional orthogonal filter banks [19, 20]...

    Yi Chenet al. ResearchArticle Design of Optimal Quincunx Filter Banks for Image Codi...

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