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

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

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

. 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

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 time-frequency localization of elements of an orthonormal basis, which improves previous

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

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

We describe extensions to the "best-basis" 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 time-frequency energy

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

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