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Abul Hasan Siddiqi - One of the best experts on this subject based on the ideXlab platform.
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WAVELETS ASSOCIATED WITH NONUNIFORM Multiresolution Analysis ON POSITIVE HALF-LINE
Industrial and Applied Mathematics, 2019Co-Authors: Yu. A. Farkov, Pammy Manchanda, Abul Hasan SiddiqiAbstract:Gabardo and Nashed [Nonuniform Multiresolution Analysis and spectral pairs, J. Funct. Anal.158 (1998) 209–241] introduced the Nonuniform Multiresolution Analysis (NUMRA) whose translation set is not a group. Farkov [Orthogonal p-wavelets on ℝ+, in Proc. Int. Conf. Wavelets and Splines (St. Petersburg State University, St. Petersburg, 2005), pp. 4–26] studied Multiresolution Analysis (MRA) on positive half line and constructed associated wavelets. Meenakshi et al. [Wavelets associated with Nonuniform Multiresolution Analysis on positive half line, Int. J. Wavelets, Multiresolut. Inf. Process.10(2) (2011) 1250018, 27pp.] studied NUMRA on positive half line and proved the analogue of Cohen's condition for the NUMRA on positive half line. We construct the associated wavelet packets for such an MRA and study its properties.
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Wavelets associated with vector-valued nonuniform Multiresolution Analysis
Applicable Analysis, 2013Co-Authors: Meenakshi, Pammy Manchanda, Abul Hasan SiddiqiAbstract:We consider a generalization of the notion of non-uniform Multiresolution Analysis (NUMRA) which is called vector-valued non-uniform Multiresolution Analysis (VNUMRA). The concept of NUMRA was introduced by Gabardo and Nashed based on the theory of spectral pairs. Xia and Suter introduced vector-valued Multiresolution Analysis and orthogonal vector-valued wavelets. We introduce VNUMRA where the associated subspace of has, an orthonormal basis, a collection of translates of a vector-valued function of the form where , is an integer and is an odd integer with such that and are relatively prime and is the set of all integers and the corresponding dilation factor is . We obtain the necessary and sufficient condition for the existence of associated wavelets and present a construction of VNUMRA.
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WAVELETS ASSOCIATED WITH NONUNIFORM Multiresolution Analysis ON POSITIVE HALF-LINE
International Journal of Wavelets Multiresolution and Information Processing, 2012Co-Authors: Meenakshi, Pammy Manchanda, Abul Hasan SiddiqiAbstract:Gabardo and Nashed have studied nonuniform Multiresolution Analysis based on the theory of spectral pairs in a series of papers, see Refs. 4 and 5. Farkov,3 has extended the notion of Multiresolution Analysis on locally compact Abelian groups and constructed the compactly supported orthogonal p-wavelets on L2(ℝ+). We have considered the nonuniform Multiresolution Analysis on positive half-line. The associated subspace V0 of L2(ℝ+) has an orthonormal basis, a collection of translates of the scaling function φ of the form {φ(x ⊖ λ)}λ∈Λ+ where Λ+ = {0, r/N} + ℤ+, N > 1 (an integer) and r is an odd integer with 1 ≤ r ≤ 2N - 1 such that r and N are relatively prime and ℤ+ is the set of non-negative integers. We find the necessary and sufficient condition for the existence of associated wavelets and derive the analogue of Cohen's condition for the nonuniform Multiresolution Analysis on the positive half-line.
María Luisa Gordillo - One of the best experts on this subject based on the ideXlab platform.
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Irregular Multiresolution Analysis and associated wavelet
Arabian Journal of Mathematics, 2014Co-Authors: María Luisa GordilloAbstract:We introduce two generalizations, the first of which generalizes the concept of Multiresolution Analysis. We define the irregular generalized Multiresolution Analysis (IGMRA). This structure is defined taking translations on sets that are not necessarily regular lattices, for which certain density requirements are required, and without using dilations, also allows each subspace of IGMRA to be generated by outer frames of translations of different functions. The second generalization concerns the concept of association of wavelets to these new structures. We take frames of translations of a countable set of functions, which we called generalized wavelets , and define the concept of association of these generalized wavelets to those previously defined IGMRA. In the next stage, we prove two existence theorems. In the first theorem, we prove existence of IGMRA, and in the second existence of generalized wavelets associated with it. In the latter, we show that we are able to associate frames of translations with optimal localization properties, to IGMRA. In the last section of this paper, concrete examples of these structures are presented for L 2 ( R ) and for L 2 ( R 2 ) .
Pammy Manchanda - One of the best experts on this subject based on the ideXlab platform.
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WAVELETS ASSOCIATED WITH NONUNIFORM Multiresolution Analysis ON POSITIVE HALF-LINE
Industrial and Applied Mathematics, 2019Co-Authors: Yu. A. Farkov, Pammy Manchanda, Abul Hasan SiddiqiAbstract:Gabardo and Nashed [Nonuniform Multiresolution Analysis and spectral pairs, J. Funct. Anal.158 (1998) 209–241] introduced the Nonuniform Multiresolution Analysis (NUMRA) whose translation set is not a group. Farkov [Orthogonal p-wavelets on ℝ+, in Proc. Int. Conf. Wavelets and Splines (St. Petersburg State University, St. Petersburg, 2005), pp. 4–26] studied Multiresolution Analysis (MRA) on positive half line and constructed associated wavelets. Meenakshi et al. [Wavelets associated with Nonuniform Multiresolution Analysis on positive half line, Int. J. Wavelets, Multiresolut. Inf. Process.10(2) (2011) 1250018, 27pp.] studied NUMRA on positive half line and proved the analogue of Cohen's condition for the NUMRA on positive half line. We construct the associated wavelet packets for such an MRA and study its properties.
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Wavelets associated with vector-valued nonuniform Multiresolution Analysis
Applicable Analysis, 2013Co-Authors: Meenakshi, Pammy Manchanda, Abul Hasan SiddiqiAbstract:We consider a generalization of the notion of non-uniform Multiresolution Analysis (NUMRA) which is called vector-valued non-uniform Multiresolution Analysis (VNUMRA). The concept of NUMRA was introduced by Gabardo and Nashed based on the theory of spectral pairs. Xia and Suter introduced vector-valued Multiresolution Analysis and orthogonal vector-valued wavelets. We introduce VNUMRA where the associated subspace of has, an orthonormal basis, a collection of translates of a vector-valued function of the form where , is an integer and is an odd integer with such that and are relatively prime and is the set of all integers and the corresponding dilation factor is . We obtain the necessary and sufficient condition for the existence of associated wavelets and present a construction of VNUMRA.
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WAVELETS ASSOCIATED WITH NONUNIFORM Multiresolution Analysis ON POSITIVE HALF-LINE
International Journal of Wavelets Multiresolution and Information Processing, 2012Co-Authors: Meenakshi, Pammy Manchanda, Abul Hasan SiddiqiAbstract:Gabardo and Nashed have studied nonuniform Multiresolution Analysis based on the theory of spectral pairs in a series of papers, see Refs. 4 and 5. Farkov,3 has extended the notion of Multiresolution Analysis on locally compact Abelian groups and constructed the compactly supported orthogonal p-wavelets on L2(ℝ+). We have considered the nonuniform Multiresolution Analysis on positive half-line. The associated subspace V0 of L2(ℝ+) has an orthonormal basis, a collection of translates of the scaling function φ of the form {φ(x ⊖ λ)}λ∈Λ+ where Λ+ = {0, r/N} + ℤ+, N > 1 (an integer) and r is an odd integer with 1 ≤ r ≤ 2N - 1 such that r and N are relatively prime and ℤ+ is the set of non-negative integers. We find the necessary and sufficient condition for the existence of associated wavelets and derive the analogue of Cohen's condition for the nonuniform Multiresolution Analysis on the positive half-line.
John J. Benedetto - One of the best experts on this subject based on the ideXlab platform.
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ICASSP (3) - Multiresolution Analysis frames with applications
IEEE International Conference on Acoustics Speech and Signal Processing, 1993Co-Authors: John J. BenedettoAbstract:A generalization of Multiresolution Analysis (MRA) to arbitrary affine frames, and the constructions of affine frames based on MRAs are considered and characterized. The authors define a frame Multiresolution Analysis (FMRA) and provide a necessary and sufficient condition for constructing frames of translates. Conditions for constructing FMRAs and associated frames are derived. The results are part of the theoretical background for multiscale signal processing problems including filter bank design, where redundancy and robustness play a role. >
Meenakshi - One of the best experts on this subject based on the ideXlab platform.
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Wavelets associated with vector-valued nonuniform Multiresolution Analysis
Applicable Analysis, 2013Co-Authors: Meenakshi, Pammy Manchanda, Abul Hasan SiddiqiAbstract:We consider a generalization of the notion of non-uniform Multiresolution Analysis (NUMRA) which is called vector-valued non-uniform Multiresolution Analysis (VNUMRA). The concept of NUMRA was introduced by Gabardo and Nashed based on the theory of spectral pairs. Xia and Suter introduced vector-valued Multiresolution Analysis and orthogonal vector-valued wavelets. We introduce VNUMRA where the associated subspace of has, an orthonormal basis, a collection of translates of a vector-valued function of the form where , is an integer and is an odd integer with such that and are relatively prime and is the set of all integers and the corresponding dilation factor is . We obtain the necessary and sufficient condition for the existence of associated wavelets and present a construction of VNUMRA.
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WAVELETS ASSOCIATED WITH NONUNIFORM Multiresolution Analysis ON POSITIVE HALF-LINE
International Journal of Wavelets Multiresolution and Information Processing, 2012Co-Authors: Meenakshi, Pammy Manchanda, Abul Hasan SiddiqiAbstract:Gabardo and Nashed have studied nonuniform Multiresolution Analysis based on the theory of spectral pairs in a series of papers, see Refs. 4 and 5. Farkov,3 has extended the notion of Multiresolution Analysis on locally compact Abelian groups and constructed the compactly supported orthogonal p-wavelets on L2(ℝ+). We have considered the nonuniform Multiresolution Analysis on positive half-line. The associated subspace V0 of L2(ℝ+) has an orthonormal basis, a collection of translates of the scaling function φ of the form {φ(x ⊖ λ)}λ∈Λ+ where Λ+ = {0, r/N} + ℤ+, N > 1 (an integer) and r is an odd integer with 1 ≤ r ≤ 2N - 1 such that r and N are relatively prime and ℤ+ is the set of non-negative integers. We find the necessary and sufficient condition for the existence of associated wavelets and derive the analogue of Cohen's condition for the nonuniform Multiresolution Analysis on the positive half-line.
