Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.

Biorthogonal M -Channel Compactly Supported Wavelets

Abstract: We study a class of M -channel subband coding schemes with perfect reconstruction. Along the lines of [8] and [10], we construct compactly supported biorthogonal wavelet bases of L2(R) , with dilation factor M , associated to these schemes. In particular, we study the case of splines, and obtain explicitly simple expressions for all the relevant filters. The resulting wavelets have arbitrarily large regularity and we also obtain asymptotic estimates for the regularity exponent.

Four-Dimensional Compact Manifolds with Nonnegative Biorthogonal Curvature

Abstract: The goal of this article is to study the pinching problem proposed by S.-T. Yau in 1990 replacing sectional curvature by one weaker condition on biorthogonal curvature. Moreover, we classify 4-dimensional compact oriented Riemannian manifolds with nonnegative biorthogonal curvature. In particular, we obtain a partial answer to Yau Conjecture on pinching theorem for 4-dimensional compact manifolds.

A new approach to the design of biorthogonal triplet half-band filter banks using generalized half-band polynomials

Abstract: This paper presents a novel approach to design a class of biorthogonal triplet half-band filter banks based on the generalized half-band polynomials. The filter banks are designed with the help of three-step lifting scheme (using three kernels). The generalized half-band polynomial is used to construct these three kernels by imposing the number of zeros at $$z=-1$$ . The maximum number of zeros imposed for the three kernels is half of the order of half-band polynomial ( $$K/2$$ for $$K$$ order polynomial). The three kernels give a set of constraints on the coefficients of half-band polynomial by imposing the zeros. In addition to structural perfect reconstruction and linear phase, the proposed filter banks provide better frequency selectivity, more similarity between analysis and synthesis filters (measure of near-orthogonality), and good time–frequency localization. The proposed technique offers more flexibility in the design of filters using two degrees of freedom. Some examples have been presented to illustrate the method.

Semi-regular biorthogonal pairs and generalized Riesz bases

Abstract: In this paper we introduce general theories of semi-regular biorthogonal pairs, generalized Riesz bases and its physical applications. Here we deal with biorthogonal sequences {ϕn} and {ψn} in a Hilbert space H , with domains D ( ϕ ) = { x ∈ H ; ∑ k = 0 ∞ ( x | ϕ k ) 2 < ∞ } and D ( ψ ) = { x ∈ H ; ∑ k = 0 ∞ ( x | ψ k ) 2 < ∞ } and linear spans Dϕ ≡ Span{ϕn} and Dψ ≡ Span{ψn}. A biorthogonal pair ({ϕn}, {ψn}) is called regular if both Dϕ and Dψ are dense in H , and it is called semi-regular if either Dϕ and D(ϕ) or Dψ and D(ψ) are dense in H . In a previous paper [H. Inoue, J. Math. Phys. 57, 083511 (2016)], we have shown that if ({ϕn}, {ψn}) is a regular biorthogonal pair then both {ϕn} and {ψn} are generalized Riesz bases defined in the work of Inoue and Takakura [J. Math. Phys. 57, 083505 (2016)]. Here we shall show that the same result holds true if the pair is only semi-regular by using operators Tϕ,e, Te,ϕ, Tψ,e, and Te,ψ defined by an orthonormal basis e in H and a biorthogonal pair ({ϕn}, {ψn}). F...