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Orthonormal bases of compactly supported wavelets
, 1993
"... Several variations are given on the construction of orthonormal bases of wavelets with compact support. They have, respectively, more symmetry, more regularity, or more vanishing moments for the scaling function than the examples constructed in Daubechies [Comm. Pure Appl. Math., 41 (1988), pp. 90 ..."
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Cited by 2205 (27 self)
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Several variations are given on the construction of orthonormal bases of wavelets with compact support. They have, respectively, more symmetry, more regularity, or more vanishing moments for the scaling function than the examples constructed in Daubechies [Comm. Pure Appl. Math., 41 (1988), pp
Orthonormal Bases for System Identification
"... In this paper we present a general and very simple construction for generating complete orthonormal bases for system identification. This construction provides a unifying formulation of orthonormal bases since the common FIR and recently popular Laguerre and Kautz model structures are restrictive sp ..."
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In this paper we present a general and very simple construction for generating complete orthonormal bases for system identification. This construction provides a unifying formulation of orthonormal bases since the common FIR and recently popular Laguerre and Kautz model structures are restrictive
The Utility of Orthonormal Bases
, 1998
"... There has been recent interest in using orthonormalised forms of fixed denominator model structures for system identification. However, modulo numerical conditioning considerations, the transfer function estimates obtained by using these sometimes complex to implement structures are identical to tha ..."
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Cited by 1 (0 self)
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orthonormally parameterised model structures in a system identification setting. Technical Report EE9802, Department of Electrical and Computer Engineering, University of Newcastle,AUSTRALIA 1 Introduction There has been a recent explosion of interest in the use of rational orthonormal bases in system
Smooth Localized Orthonormal Bases
, 1992
"... . We describe an orthogonal decomposition of L 2 (R) which maps smooth functions to smooth periodic functions. It generalizes previous constructions by Malvar, Coifman and Meyer. The adjoint of the decomposition can be used to construct smooth orthonormal windowed exponential, wavelet and wavelet ..."
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Cited by 9 (0 self)
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. We describe an orthogonal decomposition of L 2 (R) which maps smooth functions to smooth periodic functions. It generalizes previous constructions by Malvar, Coifman and Meyer. The adjoint of the decomposition can be used to construct smooth orthonormal windowed exponential, wavelet and wavelet
UNCERTAINTY PRINCIPLES FOR ORTHONORMAL BASES
, 2006
"... Abstract. In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the timefrequency localization of elements of an orthonormal basis, which improves previous unpubli ..."
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Cited by 5 (0 self)
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Abstract. In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the timefrequency localization of elements of an orthonormal basis, which improves previous
Orthonormal bases with nonlinear phases
 ADV COMPUT MATH
, 2009
"... For adaptive representation of nonlinear signals, the bank M of real square integrable functions that have nonlinear phases and nonnegative instantaneous frequencies under the analytic signal method is investigated. A particular class of functions with explicit expressions in M is obtained using ..."
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Cited by 6 (4 self)
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For adaptive representation of nonlinear signals, the bank M of real square integrable functions that have nonlinear phases and nonnegative instantaneous frequencies under the analytic signal method is investigated. A particular class of functions with explicit expressions in M is obtained using
ORTHONORMAL BASES OF HILBERT SPACES
, 908
"... Assume H is a Hilbert space and K is a dense linear (not necessarily closed) subspace. The question whether K necessarily contains an orthonormal basis for H even when H is nonseparable was mentioned by Bruce Blackadar in an informal conversation during the Canadian Mathematical Society meeting in O ..."
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of the continuum and the least ordinal of this cardinality. All bases are orthonormal. For cardinals λ < θ consider ℓ 2 (λ) as a subspace of ℓ 2 (θ) consisting of vectors supported on the first λ coordinates. Let pλ denote the projection of ℓ 2 (θ) to ℓ 2 (λ). Lemma 1. Assume λ < θ are infinite cardinals
On Local Orthonormal Bases For Classification And Regression
 Comptes Rendus Acad. Sci. Paris, Serie I
, 1995
"... We describe extensions to the "bestbasis" method to select orthonormal bases suitable for signal classification and regression problems from a large collection of orthonormal bases. For classification problems, we select the basis which maximizes relative entropy of timefrequency energy ..."
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We describe extensions to the "bestbasis" method to select orthonormal bases suitable for signal classification and regression problems from a large collection of orthonormal bases. For classification problems, we select the basis which maximizes relative entropy of timefrequency energy
A Unifying Construction of Orthonormal Bases for System Identification
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1994
"... In this paper we develop a general and very simple construction for complete orthonormal bases for system identification. This construction provides a unifying formulation of all known orthonormal bases since the common FIR and recently popular Laguerre and Kautz model structures are restrictive spe ..."
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Cited by 78 (20 self)
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In this paper we develop a general and very simple construction for complete orthonormal bases for system identification. This construction provides a unifying formulation of all known orthonormal bases since the common FIR and recently popular Laguerre and Kautz model structures are restrictive
ORTHONORMAL BASES OF EXPONENTIALS FOR THE nCUBE
 VOL. 103, NO. 1 DUKE MATHEMATICAL JOURNAL
, 2000
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