Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
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TL;DR: A new speaker feature extracted from wavelet decomposition using biorthogonal Riesz bases is described, showing better performance than the other wavelet transforms with respect to the percentages of recognition.
15 citations
TL;DR: A new numerical approach for finding the solution of linear time‐delay control systems with a quadratic performance index using new hybrid functions based on a hybrid of block‐pulse functions and biorthogonal multiwavelets that consist of cubic Hermite splines on the primal side.
15 citations
TL;DR: This paper provides a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form of a finitely supported sequence of r × r matrices called the refinement mask.
Abstract: Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis. In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form
$$\varphi (x) = \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )\varphi (Mx - \alpha ), x \in \mathbb{R}^s } ,$$
where the vector of functions ϕ = (ϕ
1, …, ϕ
r)T is in
$$(L_2 (\mathbb{R}^s ))^r ,a = :(a(\alpha ))_{\alpha \in \mathbb{Z}^s } $$
is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim
n→∞
M
−n
= 0. Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.
15 citations
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TL;DR: In this article, the effect of purely non-Hermitian disorders, a combination of these two ingredients, in a 1D chiral symmetric lattice with disordered gain and loss was considered.
Abstract: Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients, in a 1D chiral symmetric lattice with disordered gain and loss. The increasing disorder strength can drive a transition from trivial to topological insulators, characterizing by the change of topological winding number defined by localized states in the gapless and complex bulk spectra. The non-Hermitian critical behaviors are characterized by the biorthogonal localization length of zero energy edge modes, which diverges at the critical transition point and establishes the bulk-edge correspondence. Furthermore, we show that the bulk topology may be experimentally accessed by measuring the biorthogonal chiral displacement $\mathcal{C}$, which converges to the winding number through time-averaging and can be extracted from proper Ramsey-interference sequences. We propose a scheme to implement and probe such non-Hermitian disorder driven topological insulators using photons in coupled micro-cavities.
15 citations
TL;DR: In this article, a space curved surface shape reconstruction algorithm is proposed for shape perception and reconstruction of flexible plate structure, based on biorthogonal strain data measured by optimal distribution.
Abstract: A space curved surface shape reconstruction algorithm is proposed for shape perception and reconstruction of flexible plate structure. First, biorthogonal strain data measured by optimal distribute...
15 citations