Wyniki wyszukiwania - BazTech

1

Prefiltering in Wavelet Analysis Applying Cubic B-Splines

Rakowski W.

International Journal of Electronics and Telecommunications

|

2014

|

Vol. 60, No. 4

331-340

EN

Wavelet transform algorithms (Mallat’s algorithm, a trous algorithm) require input data in the form of a sequence of numbers equal to the signal projection coefficients on a space spanned by integer-translated copies of a scaling function. After sampling of the continuous-time signal, it is most frequently possible to compute only approximated values of the signal projection coefficients by choosing a specific signal approximation. Calculation of the signal projection coefficients based on the signal interpolation by means of cubic B-splines is proposed in the paper.

2

Invariant measures whose supports possess the strong open set property

Goodman G. S.

Opuscula Mathematica

|

2008

|

Vol. 28, no. 4

471-480

EN

Let X be a complete metric space, and S the union of a finite number of strict contractions on it. If P is a probability distribution on the maps, and K is the fractal determined by S, there is a unique Borel probability measure µp on X which is invariant under the associated Markov operator, and its support is K. The Open Set Condition (OSC) requires that a non-empty, subinvariant, bounded open set V⊂ X exists whose images under the maps are disjoint; it is strong if K ∩ V ≠ 0.In that case, the core of [formula] is non-empty and dense in K. Moreover, when X is separable, V has full µp-measure for every P. We show that the strong condition holds for V satisfying the OSC iff µp(ϑV) = 0, and we prove a zero-one law for it. We characterize the complement of V relative to K, and we establish that the values taken by invariant measures on cylinder sets defined by K, or by the closure of V, form multiplicative cascades.

3

Fractal sets satisfying the strong open set condition in complete metric spaces

Goodman G. S.

Opuscula Mathematica

|

2008

|

Vol. 28, no. 4

463-470

EN

Let K be a Hutchinson fractal in a complete metric space X, invariant under the action S of the union of a finite number of Lipschitz contractions. The Open Set Condition states that X has a non-empty subinvariant bounded open subset V, whose images under the maps are disjoint. It is said to be strong if V meets K. We show by a category argument that when K ⊄ V and the restrictions of the contractions to V are open, the strong condition implies that [formula] termed the core of V, is non-empty. In this case, it is an invariant, proper, dense, subset of K, made up of points whose addresses are unique. Conversely, [formula] implies the SOSC, without any openness assumption.

4

Some new examples of wavelets in the Hardy space [H^2](R)

Majchrowska G.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2001

|

Vol. 49, no 2

141-149

EN

In this paper we get some new examples of wavelet sets and scaling sets in [H^2](R). In particular we prove that there exists a wavelet which does not belong to any [L^p](R) for p < 2.