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Keywords
(13)
Cayley Transform
Design Method
Filter Design
Finite Impulse Response
Fir Filter
Hermitian Matrices
Higher Dimensions
Indexing Terms
Linear Constraint
Nonlinear Equation
Spectral Factorization
Filter Bank
Infinite Impulse Response
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Skew symmetry and orthogonality in the equivalent representation problem of a timevarying multiport inductor
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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
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Multidimensional orthogonal filter bank characterization and design using the Cayley transform
(
Citations: 11
)
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Jianping Zhou
,
Minh N. Do
,
Jelena Kovacevic
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 onedimensional 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 onetoone mapping be tween paraunitary matrices and paraskewHermitian matrices. In contrast to the paraunitary condition, the paraskewHermitian 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. 760769, 2005
DOI:
10.1109/TIP.2005.847323
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Citation Context
(5)
...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 2D Nearly Orthogonal Filter Ba...
...Twodimensional (2D) 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. Hung
,
et al.
Design of Diamond and Circular Filters by Semidefinite Programming
...<{[SECTION]}>of intensive research (see e.g. [4, 8,
15
] and the references...
T. Q. Hung
,
et al.
SDP for 2d 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 paraskewHermitian (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 Zhou
,
et 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 Chen
,
et al.
ResearchArticle Design of Optimal Quincunx Filter Banks for Image Codi...
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Citations
(11)
Twochannel nonseparable wavelets statistically matched to 2D images
Anubha Gupta
,
Shiv Dutt Joshi
Journal:
Signal Processing
, vol. 91, no. 4, pp. 673689, 2011
Construction and Application of Multi dimensional Wavelets Using Gröbner Basis
Xiaoxiong Li
,
Li Wu
,
Xinfa Dong
Conference:
International Conference on MultiMedia and Information Technology  MMIT
, 2010
A Moulding Technique for the Design of 2D Nearly Orthogonal Filter Banks
Bogdan Dumitrescu
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IEEE Signal Processing Letters  IEEE SIGNAL PROCESS LETT
, vol. 17, no. 3, pp. 261264, 2010
Image zerowatermarking algorithm based on Contourlet transform and singular value decomposition: Image zerowatermarking algorithm based on Contourlet transform and singular value decomposition
Fanjuan ZENG
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Journal of Computer Applications
, vol. 28, no. 8, pp. 20332035, 2008
Design of Optimal Quincunx Filter Banks for Image Coding
(
Citations: 6
)
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