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Biorthogonal system

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


Papers
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Journal ArticleDOI
TL;DR: The analysis of low-delay, biorthogonal filterbanks; shows that prototypes solely designed to minimize the stopband energy may lead to wide open frames and, thus, to an undesirable numerical behavior.
Abstract: This paper addresses the efficient computation of frame bounds for cosine-modulated filterbanks. We derive explicit expressions for the eigenvalues of the frame operator that can be easily computed from the prototype's polyphase components. The number of channels and the downsampling factor may be even or odd, and the oversampling factor is supposed to be an integer. The analysis of low-delay, biorthogonal filterbanks; shows that prototypes solely designed to minimize the stopband energy may lead to wide open frames and, thus, to an undesirable numerical behavior. Because the computational cost of determining the frame bounds with the proposed method is very low, we can directly use the bounds during prototype optimization and obtain prototypes with minimum stopband energy under the condition of fixed frame bounds. Various design examples are presented.

13 citations

Journal ArticleDOI
TL;DR: An extended version of pseudofermions based on biorthogonal bases in a finitedimensional Hilbert space is discussed and some examples in detail are described.
Abstract: We review some basic definitions and a few facts recently established for D-pseudobosons and pseudofermions. We also discuss an extended version of pseudofermions based on biorthogonal bases in a finitedimensional Hilbert space and describe some examples in detail.

13 citations

Journal ArticleDOI
30 Dec 2017
TL;DR: In this article, the effects of dissipation are effectively described by PT-symmetric potentials, and a general numerical gauge smoothing procedure is developed to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian.
Abstract: We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by PT -symmetric potentials. In this framework we develop a general numerical gauge smoothing procedure to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional PT -symmetric lattice system and verify our numerical results by an analytical calculation.

13 citations

Proceedings ArticleDOI
23 Oct 1996
TL;DR: This approach to off-line optical character recognition for hand-written or printed characters using for feature extraction and classification biorthogonal discrete wavelet transform achieves great recognition accuracy and font insensitivity requiring only a small training set of characters.
Abstract: We present an approach to off-line optical character recognition for hand-written or printed characters using for feature extraction and classification biorthogonal discrete wavelet transform. Our aim is to optimize character recognition methods independently of printing styles, writing styles and fonts used. Characters are identified with their contours, thus characterized from their curvature function. Curvature function is used for feature extraction while classification is accomplished by LVQ algorithms. This method achieves great recognition accuracy and font insensitivity requiring only a small training set of characters.

13 citations

Journal ArticleDOI
TL;DR: A flexible and efficient wavelet construction for non-uniform B-spline curves and surfaces that allows to remove knots in arbitrary order minimizing the displacement of control points when a knot is re-inserted.

13 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202329
2022105
202155
202058
201960