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33rd IEEE International Conference on Acoustics, Speech and Signal Processing

作者： De Meuleneire, M. Taddei, H. Pastor, D. Nokia Siemens Networks COO RTP PT HWCT Comp Techn SDE Otto Hahn Ring 6 D-81739 Munich Germany ENST Bretagne Technop Brest Iroise Dept SC F-29238 Brest 3 France

ISBN: (纸本)9781424414833

This paper proposes a new quantization for transform coefficients based on algebraic quantization. The coefficients are represented by a few pulses multiplied by a unique amplitude. The coefficients to be transmitted are selected by optimizing an error criterion, that determines the signs, positions and amplitudes of the pulses. This simple quantization has been implemented in a wavelet-based wideband scalable coder, and has been proved to provide a perceptually better quality than SPIHT on speech signal and music.

关键词： embedded coding transform coding algebraic quantization

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Refined algebraic quantization with the triangular subgroup of SL(2, R)

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INTERNATIONAL JOURNAL OF MODERN PHYSICS D 2005年第7期14卷 1131-1157页

作者： Louko, J Molgado, A Univ Nottingham Sch Math Sci Nottingham NG7 2RD England

We investigate refined algebraic quantization with group averaging in a constrained Hamiltonian system whose gauge group is the connected component of the lower triangular subgroup of SL(2,R). The unreduced phase space is T*Rp+q, with p >= 1 and q >= 1, and the system has a distinguished classical o(p,q) observable algebra. Group averaging with the geometric average of the right and left invariant measures, invariant under the group inverse, yields a Hilbert space that carries a maximally degenerate principal unitary series representation of O(p,q). The representation is nontrivial iff (p,q)not equal(1,1), which is also the condition for the classical reduced phase space to be a symplectic manifold up to a singular subset of measure zero. We present a detailed comparison to an algebraic quantization that imposes the constraints in the sense (H) over cap (alpha)Psi=0 and postulates self-adjointness of the o(p,q) observables. Under certain technical assumptions that parallel those of the group averaging theory, this algebraic quantization gives no quantum theory when (p,q)=(1,2) or (2,1), or when p >= 2, q >= 2 and p+q equivalent to 1 (mod 2).

关键词： refined algebraic quantization algebraic quantization group averaging mini-superspace quantum gravity

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Wavelet scalable speech coding using algebraic quantization

Wavelet scalable speech coding using algebraic quantization

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33rd IEEE International Conference on Acoustics, Speech and Signal Processing

作者： De Meuleneire, M. Taddei, H. Pastor, D. Nokia Siemens Networks COO RTP PT HWCT Comp Techn SDE Otto Hahn Ring 6 D-81739 Munich Germany ENST Bretagne Technop Brest Irois Dept SC F-29238 Brest 3 France

ISBN: (纸本)9781424414833

This paper proposes a new structure for a scalable codec. Our proposed codec works with 10 ms input frame for wideband speech and audio signals at bit rates ranging from 8 to 32 kbit/s. The core layer is the ITU-T G.729 at 8 kbit/s producing a narrowband output. The first enhancement layer is a band-witdh extension providing a wideband output with 2 kbit/s. The second enhancement layer is based on algebraic quantization of wavelet packet coefficients and improves gradually the synthesized signal as the bitrate increases. For speech signals, at bitrates of 24 and 32 kbit/s, the codec is shown to be equivalent to the ITU-T G.722 codec at 56 and 64 kbit/s, respectively. Moreover, the codec at 32 kbit/s is assessed to be equivalent to the recently standardized embedded codec ITU-T G.729.1 at the same bitrate with a lower algorithmic delay.

关键词： embedded coding linear predictive coding bandwidth extension wavelets algebraic quantization

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The Embedded Audio Coding of algebraic quantization Based on the Transform Coefficients

The Embedded Audio Coding of Algebraic Quantization Based on...

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2nd International Conference on Mechanical Engineering and Green Manufacturing (MEGM 2012)

作者： Tang, Gang Huangshi Inst Technol Huangshi 435003 Peoples R China

ISBN: (纸本)9783037853771

This paper proposes a new quantitative method called the transform coefficients, which is based on the algebraic quantization method. This coefficient is defined as a unique amplitude multiplied by a number of *** order to determine the signs of pulse, location and amplitude, we selected the transmission coefficient by adopting an ideal standard errors. This simple quantification has been implemented in scalable coding of microwave transform, and has been proved that its voice signal and music effect is better than that of the SPIHT.

关键词： Embedded coding Audio coding algebraic quantization

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On the algebraic quantization of a massive scalar field in anti-de Sitter spacetime

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REVIEWS IN MATHEMATICAL PHYSICS 2018年第2期30卷

作者： Dappiaggi, Claudio Ferreira, Hugo R. C. Univ Pavia Dipartimento Fis Via Bassi6 I-27100 Pavia Italy Ist Nazl Fis Nucl Sez Pavia Via Bassi6 I-27100 Pavia Italy

We discuss the algebraic quantization of a real, massive scalar field in the Poincare patch of the (d+1)-dimensional anti-de Sitter spacetime, with arbitrary boundary conditions. By using the functional formalism, we show that it is always possible to associate to such system an algebra of observables enjoying the standard properties of causality, time-slice axiom and F-locality. In addition, we characterize the wavefront set of the ground state associated to the system under investigation. As a consequence, we are able to generalize the definition of Hadamard states and construct a global algebra of Wick polynomials.

关键词： Anti-de Sitter algebraic quantization Hadamard state

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Finite dimensional Hopf actions on algebraic quantizations

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ALGEBRA & NUMBER THEORY 2016年第10期10卷 2287-2310页

作者： Etingof, Pavel Walton, Chelsea MIT Dept Math 77 Massachusetts Ave Cambridge MA 02139 USA Temple Univ Dept Math 1805 N Broad St Philadelphia PA 19122 USA

Let k be an algebraically closed field of characteristic zero. In joint work with J. Cuadra, we showed that a semisimple Hopf action on a Weyl algebra over a polynomial algebra k [z(1)......z(s)] factors through a group action, and this in fact holds for any finite dimensional Hopf action if s = 0. We also generalized these results to finite dimensional Hopf actions on algebras of differential operators. In this work we establish similar results for Hopf actions on other algebraic quantizations of commutative domains. This includes universal enveloping algebras of finite dimensional Lie algebras, spherical symplectic reflection algebras, quantum Hamiltonian reductions of Weyl algebras (in particular, quantized quiver varieties), finite W-algebras and their central reductions, quantum polynomial algebras, twisted homogeneous coordinate rings of abelian varieties, and Sklyanin algebras. The generalization in the last three cases uses a result from algebraic number theory due to A. Perucca.

关键词： algebraic quantization filtered deformation Hopf algebra action quantum polynomial algebra Sklyanin algebra twisted coordinate ring

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quantization on a torus without position operators

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MODERN PHYSICS LETTERS A 2003年第38期18卷 2755-2765页

作者： Tanimura, S Osaka City Univ Grad Sch Engn Sumiyoshi Ku Osaka 5588585 Japan

We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct an irreducible representation of the algebra. We show that it realizes quantum mechanics of a charged particle in a uniform magnetic field and prove that any irreducible representation of the algebra is unitarily equivalent to each other. This work provides a firm foundation for the noncommutative torus theory.

关键词： torus algebraic quantization representation theory

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quantization of length in spaces with position-dependent noncommutativity

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INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS 2024年第14期21卷

作者： Aryampilly, Jishnu Balasundaram, Muthukumar Rashid, Aamir Pondicherry Univ Sch Phys Chem & Appl Sci Kalapet 605014 Puducherry India

In this paper, we present a novel approach to quantizing the length in noncommutative spaces with positional-dependent noncommutativity. The method involves constructing ladder operators that change the length not only along a plane but also along the third direction due to a noncommutative parameter that is a combination of canonical/Weyl-Moyal-type and Lie algebraic-type. The primary quantization of length in canonical-type noncommutative space takes place only on a plane, while in the present case, it happens in all three directions. We establish an operator algebra that allows for the raising or lowering of eigenvalues of the operator corresponding to the square of the length. We also attempt to determine how the obtained ladder operators act on different states and work out the eigenvalues of the square of the length operator in terms of eigenvalues corresponding to the ladder operators. We conclude by discussing the results obtained.

关键词： Noncommutative spaces position-dependent noncommutativity algebraic quantization length quantization

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