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, two physical examples of the pseudo-bosons, recently introduced in connection with pseudo-hermitian quantum mechanics, are discussed, and the authors show that the extended harmonic oscillator and the Swanson model satisfy all the assumptions of the pseudosonic framework introduced by the author.
64 citations
TL;DR: This paper introduces the most general degree-one Cafacafi building block, and considers the problem of factorizing cafacafi systems into these building blocks.
Abstract: For pt. I see ibid., vol.43, no.5, p.1090, 1990. In part I we studied the system-theoretic properties of discrete time transfer matrices in the context of inversion, and classified them according to the types of inverses they had. In particular, we outlined the role of causal FIR matrices with anticausal FIR inverses (abbreviated cafacafi) in the characterization of FIR perfect reconstruction (PR) filter banks. Essentially all FIR PR filter banks can be characterized by causal FIR polyphase matrices having anticausal FIR inverses. In this paper, we introduce the most general degree-one cafacafi building block, and consider the problem of factorizing cafacafi systems into these building blocks. Factorizability conditions are developed. A special class of cafacafi systems called the biorthogonal lapped transform (BOLT) is developed, and shown to be factorizable. This is a generalization of the well-known lapped orthogonal transform (LOT). Examples of unfactorizable cafacafi systems are also demonstrated. Finally it is shown that any causal FIR matrix with FIR inverse can be written as a product of a factorizable cafacafi system and a unimodular matrix. >
64 citations
Posted Content•
TL;DR: In this article, a general approach to infinite dimensional non-Gaussian analysis is given, which generalizes the work of KSWY95, where a family of biorthogonal systems is constructed for a given measure of Poisson type.
Abstract: We give a general approach to infinite dimensional non-Gaussian analysis which generalizes the work \cite{KSWY95}. For given measure we construct a family of biorthogonal systems. We study their properties and their Gel'fand triples that they generate. As an example we consider the measures of Poisson type.
63 citations
TL;DR: In this paper, a compactly supported biorthogonal wavelet basis adapted to some simple differential operators was constructed and the condition numbers of the corresponding stiffness matrices were estimated.
Abstract: In this paper we construct a compactly supported biorthogonal wavelet basis adapted to some simple differential operators. Moreover, we estimate the condition numbers of the corresponding stiffness matrices.
63 citations
Patent•
01 Jun 2000TL;DR: In this article, biorthogonal coding is provided in a cellular communication system in a manner that minimizes correlation of pairs of coordinates utilized in the communication system, where data that is to be communicated by a sending station is first modulated by a binary phase shift keying modulation.
Abstract: Apparatus, and an associated method, by which to form biorthogonal codes utilized in a multi-dimensional modulation scheme. In one implementation, biorthogonal coding is provided in a cellular communication system in a manner that minimizes correlation of pairs of coordinates utilized in the communication system. Data that is to be communicated by a sending station is first modulated by a binary phase shift keying modulation. These first-modulated values are used by a mapper that maps the values to selected dimension values. And, the selected dimension values into which the first-modulated values are mapped are used to select biorthogonal code values.
62 citations