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69
Tight frame characterization of multiwavelet vector functions in terms of the polyphase matrix
 Int. J. Wavelets Multiresolut. Inf. Process
, 2009
"... The extension principles play an important role in characterizing and constructing of wavelet frames. The common extension principles, the unitary extension principle (UEP) or the oblique extension principle (OEP), are based on the unitarity of the modulation matrix. In this paper we state the UEP a ..."
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Cited by 3 (0 self)
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10, 42C15. Key words. Tight frames; extension principles; polyphase representation; modulation matrix; directional wavelet frames. 1
Factoring wavelet transforms into lifting steps
 J. FOURIER ANAL. APPL
, 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
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Cited by 584 (8 self)
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. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is wellknown to algebraists (and expressed by the formula); it is also used in linear systems theory in the electrical engineering community. We
Multirate Digital Filters, Filter Banks, Polyphase Networks, and Applications: A tutorial
, 1990
"... Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This ..."
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Cited by 128 (3 self)
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and other related topics, such as block digital filtering and periodically timevarying systems, based on a pseudocirculant matrix framework, is covered. Unconventional applications of the polyphase concept are discussed.
Polyphase Filter and . . . Bidimensional Multiwavelets
, 2007
"... To construct a very smooth nonseparable multiscaling function, we impose polynomial approximation order 2 and add new conditions on the polyphase highpass filters. We work with a dilation matrix generating quincunx lattices, and fix the index set. Other imposed conditions are orthogonal filter bank ..."
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To construct a very smooth nonseparable multiscaling function, we impose polynomial approximation order 2 and add new conditions on the polyphase highpass filters. We work with a dilation matrix generating quincunx lattices, and fix the index set. Other imposed conditions are orthogonal filter
Lifting Factorization in Maple
"... Abstract This paper gives an insight into the polyphase matrix factorization by using Euclidean algorithm and its implementation in maple. The maple implementation allows the program to be called from Matlab. Polynomial reduction using Groebner bases is also incorporated into the program. This redu ..."
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Abstract This paper gives an insight into the polyphase matrix factorization by using Euclidean algorithm and its implementation in maple. The maple implementation allows the program to be called from Matlab. Polynomial reduction using Groebner bases is also incorporated into the program
Polyphase and Modulation Descriptions of Multirate Systems  A Systematic Approach
 Proc. Int. Conf. DSP
, 1995
"... International Conference on Digital Signal Processing, June 2628, 1995, Limassol, Cyprus An extended definition of discretetime linear periodically timevarying (LPTV) systems is shown to provide an elegant and systematic way of deriving zdomain polyphase and modulation descriptions of LPTV syst ..."
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Cited by 5 (0 self)
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International Conference on Digital Signal Processing, June 2628, 1995, Limassol, Cyprus An extended definition of discretetime linear periodically timevarying (LPTV) systems is shown to provide an elegant and systematic way of deriving zdomain polyphase and modulation descriptions of LPTV
Nonuniform Nonunitary Perfect Reconstruction Filter Banks for Image Coding
 in Proc. NORSIG
, 1995
"... Unitary and nonunitary filter banks with uniform frequency separation have been extensively studied in the past. Improvement in coding gain has been achieved when allowing for nonunitary filter banks in image coders. Subjective improvements can be achieved by employing nonuniform filter banks. The p ..."
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Cited by 1 (1 self)
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. The paper presents a method to construct nonuniform nonunitary perfect reconstruction filter banks. A polyphase matrix representation of nonuniform parallel filter banks is given for octave band splitting. In this case, results show that the parallel filter banks tend to become the treestructured filter
FACTORING MBAND WAVELET TRANSFORMS INTO REVERSIBLE INTEGER MAPPINGS AND LIFTING STEPS
"... In this paper, a matrix factorization method is presented for reversible integer Mband wavelet transforms. Based on an algebraic construction of orthonormal Mband wavelets with perfect reconstruction, the polyphase matrix can be factorized into a finite sequence of elementary reversible matrices t ..."
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In this paper, a matrix factorization method is presented for reversible integer Mband wavelet transforms. Based on an algebraic construction of orthonormal Mband wavelets with perfect reconstruction, the polyphase matrix can be factorized into a finite sequence of elementary reversible matrices
FACTORING MBAND WAVELET TRANSFORMS INTO REVERSIBLE INTEGER MAPPINGS AND LIFTING STEPS
"... In this paper, a matrix factorization method is presented for reversible integer Mband wavelet transforms. Based on an algebraic construction of orthonormal Mband wavelets with perfect reconstruction, the polyphase matrix can be factorized into a finite sequence of elementary reversible matrices t ..."
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In this paper, a matrix factorization method is presented for reversible integer Mband wavelet transforms. Based on an algebraic construction of orthonormal Mband wavelets with perfect reconstruction, the polyphase matrix can be factorized into a finite sequence of elementary reversible matrices
On the use of multiple constant multiplication in polyphase FIR filters and filter banks,” under review to Nordic Signal Processing Symposium
, 2004
"... Multiple constant multiplication (MCM) has been shown to be an efficient way to reduce the number of additions and subtractions in FIR filter implementations. However, for polyphase decomposed FIR filters and filter banks, the problem can be formulated in three different ways. Either as one MCM bloc ..."
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Cited by 4 (2 self)
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Multiple constant multiplication (MCM) has been shown to be an efficient way to reduce the number of additions and subtractions in FIR filter implementations. However, for polyphase decomposed FIR filters and filter banks, the problem can be formulated in three different ways. Either as one MCM
Results 1  10
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