Weaving frames have potential applications in wireless sensor networks that require distributed processing of signals under different frames. In this paper, we study some new properties weaving generalized (or g-frames) and orthonormal bases g-orthonormal bases). It is shown a g-frame its dual are woven. The inter-relation optimal bounds universal studied. Further, present characterization g-fr...

In this paper we present a general and very simple construction for generating complete orthonormal bases for system identiication. This construction provides a unifying formulation of orthonormal bases since the common FIR and recently popular Laguerre and Kautz model structures are restrictive special cases of our construction. A distinguishing feature of our construction is that it can gener...

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

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 Communicated by Qiyu Sun. Supported in part by Macau Science and Technology Fund 051/2005/A. Support...

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as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro. Finally, we show that Benedicks’ result implies that solutions of the Shrödinge...

We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).

To give exibility to the time-frequency resolution trade-o of orthonormal (ON) wavelet bases constructed by I.Daubechies [2, 1], recently multiplicityM ON wavelet bases(more generally tight frames (TFs)) have been constructedby several authors [3, 4, ?, 7, 12]. These generalizations ofthe multiplicity 2 ON wavelet bases of I. Daubechies, di erfrom the latter in that, whi...

Let B be the Borel σ-algebra of R, and let B be the Borel σ-algebra of [−∞,∞] = R ∪ {−∞,∞}: the elements of B are those subsets of R of the form B,B ∪ {−∞}, B ∪ {∞}, B ∪ {−∞,∞}, with B ∈ B. Let (X,A , μ) be a measure space. It is a fact that if fn is a sequence of A → B measurable functions then supn fn and infn fn are A → B measurable, and thus if fn is a sequence of A → B measurable functions...