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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.


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Journal ArticleDOI
TL;DR: In this paper, the authors studied affine transformations of the plane, which provide self-affine curves as attractors, and the properties of these curves depend decisively of the coefficients of the system of affnities involved.
Abstract: The objective of the present paper is the study of affine transformations of the plane, which provide self-affine curves as attractors. The properties of these curves depend decisively of the coefficients of the system of affnities involved. The corresponding functions are continuous on a compact interval. If the scale factors are properly chosen one can define Schauder bases of C[a, b] composed by affine fractal functions close to polygonals. They can be chosen bounded. The basis constants and the biorthogonal sequence of coefficient functionals are studied.

10 citations

Journal ArticleDOI
01 Nov 2001
TL;DR: A methodology for rapid silicon design of biorthogonal wavelet transform systems has been developed based on generic, scalable architectures for the forward and inverse wavelet filters, suitable for FPGA and PLD implementations.
Abstract: A methodology for rapid silicon design of biorthogonal wavelet transform systems has been developed. This is based on generic, scalable architectures for the forward and inverse wavelet filters. These architectures offer efficient hardware utilisation by combining the linear phase property of biorthogonal filters with decimation and interpolation. The resulting designs have been parameterised in terms of types of wavelet and wordlengths for data and coefficients. Control circuitry is embedded within these cores that allows them to be cascaded for any desired level of decomposition without any interface logic. The time to produce silicon designs for a biorthogonal wavelet system is only the time required to run synthesis and layout tools with no further design effort required. The resulting silicon cores produced are comparable in area and performance to hand-crafted designs. These designs are also portable across a range of foundries and are suitable for FPGA and PLD implementations.

10 citations

Journal ArticleDOI
TL;DR: In this paper, a q-analog of a pair of biorthogonal sets of rational functions which have been obtained recently by M. Rahman in connection with the addition theorem for the Hahn polynomials is obtained.
Abstract: Abstract In this note we obtain a q-analog of a pair of biorthogonal sets of rational functions which have been obtained recently by M. Rahman in connection with the addition theorem for the Hahn polynomials.

10 citations

Journal ArticleDOI
TL;DR: In this paper, a symmetric biorthogonal wavelet filter pair can be obtained by factoring the product of the complementary polynomial and the given binomial, which can then be used for image compression.
Abstract: A technique for designing new symmetric biorthogonal wavelets from a given symmetric regular filter is presented. The main idea is to find a symmetric complementary filter of a given regular filter such that it has the least mean square (LMS) amplitude deviation from the ideal halfband lowpass filter. New biorthogonal wavelet filter pairs can be obtained via factoring the product of the complementary polynomial and the given binomial. By applying these new symmetric biorthogonal wavelet filters to the compression of some complicated images an improved result in reducing artefacts may be achieved.

10 citations

Journal ArticleDOI
TL;DR: In this article, a method incorporating biorthogonal orbital optimization, symmetry projection, and double-occupancy screening with a non-unitary similarity transformation generated by the Gutzwiller factor is presented.
Abstract: We present a method incorporating biorthogonal orbital-optimization, symmetry projection, and double-occupancy screening with a non-unitary similarity transformation generated by the Gutzwiller factor [Formula: see text], and apply it to the Hubbard model. Energies are calculated with mean-field computational scaling with high-quality results comparable to coupled cluster singles and doubles. This builds on previous work performing similarity transformations with more general, two-body Jastrow-style correlators. The theory is tested on 2D lattices ranging from small systems into the thermodynamic limit and is compared to available reference data.

10 citations


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