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: In this article, the authors investigated determinantal point processes on [0, + ∞) of the form and proved that the biorthogonal polynomials associated with such models satisfy a recurrence relation and a Christoffel-Darboux formula.
Abstract: We investigate determinantal point processes on [0, +∞) of the form We prove that the biorthogonal polynomials associated with such models satisfy a recurrence relation and a Christoffel–Darboux formula if $ hetainmathbb Q$ , and that they can be characterized in terms of 1 × 2 vector-valued Riemann–Hilbert problems, which exhibit some non-standard properties. In addition, we obtain expressions for the equilibrium measure associated with our model if w(λ) = e−nV (λ) in the one-cut case with and without a hard edge
51 citations
TL;DR: A multivariable biorthogonal generalization of the Meixner, Krawtchouk, and Meixners-Pollaczek polynomials is presented in this paper.
Abstract: A multivariable biorthogonal generalization of the Meixner, Krawtchouk, and Meixner–Pollaczek polynomials is presented. It is shown that these are orthogonal with respect to subspaces of lower degree and biorthogonal within a given subspace. The weight function associated with the Krawtchouk polynomials is the multivariate binomial distribution.
51 citations
TL;DR: This paper discusses a method of regularity imposition onto biorthogonal linear-phase M-band filterbanks using the lattice structure and proposes a lifting structure for lattice matrix parameterization where regularity constraints can be imposed.
Abstract: This paper discusses a method of regularity imposition onto biorthogonal linear-phase M-band filterbanks using the lattice structure. A lifting structure is proposed for lattice matrix parameterization where regularity constraints can be imposed. The paper focuses on cases with analysis and synthesis filterbanks having up to two degrees of regularity. Necessary and sufficient conditions for regular filterbanks in terms of the filter impulse response, frequency response, scaling function, and wavelets are revisited and are derived in terms of the lattice matrices. This also leads to a constraint on the minimum filter length. Presented design examples are optimized for the purpose of image coding, i.e., the main objectives are coding gain and frequency selectivity. Simulation results from an image coding application also show that these transforms yield improvement in the perceptual quality in the reconstruction images. The approach has also been extended to the case of integer/rational lifting coefficients, which are desirable in many practical applications.
51 citations
TL;DR: An algorithm for computing optimally concentrated biorthogonal functions for the finite discrete-time Gabor expansion is developed and its merit is demonstrated via numerical simulations.
50 citations
TL;DR: An analogue of the Hahn theorem for Laurent biorthogonal polynomials (LBP) Pn(z) is studied in this article, where necessary and sufficient conditions (criterion) for derivatives P n (z) = (n + 1) −1 P′ n+1 (z).
49 citations