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A Unified Treatment of Discrete Fast Unitary Transforms

Bernard J. Fino, V. Ralph Algazi
1977 SIAM journal on computing (Print)  
A set of recursive rules which generate unitary transforms with a fast algorithm (FUT) are presented.  ...  A systematic and unified view is provided for unitary transforms which have appeared in the literature. This approach leads to a number of new transforms of potential interest.  ...  In this work we have presented a unified treatment of unitary transforms having a fast algorithm.  ... 
doi:10.1137/0206051 fatcat:gzb2zan4dbgapoug6kitvum3pi

Page 2232 of Mathematical Reviews Vol. 56, Issue 6 [page]

1978 Mathematical Reviews  
Ralph A unified treatment of discrete fast unitary transforms. SIAM J. Comput. 6 (1977), no. 4, 700-717.  ...  This paper presents a unified view of discrete unitary transforms that possess fast transform algorithms.  ... 

Orthogonal Discrete Fourier and Cosine Matrices for Signal Processing [chapter]

Daechul Park, Moon Ho
2011 Fourier Transforms - Approach to Scientific Principles  
Further investigation is needed for unified treatment of recursive decomposition of orthogonal transform matrices exploiting the properties of Jacket-like sparse matrix architecture for fast trigonometric  ...  Let's denote N -point DFT matrix as nm N N FW ⎡ ⎤ = ⎣ ⎦ ,, { 0 A sparse matrix factorization of orthogonal transforms A sparse matrix analysis of discrete Fourier transform Now we will present the  ... 
doi:10.5772/15501 fatcat:js5vv57s5vdhtevwn4aicv6is4

Sampling Theorem and Discrete Fourier Transform on the Hyperboloid

M. Calixto, J. Guerrero, J. C. Sánchez-Monreal
2010 Journal of Fourier Analysis and Applications  
We provide a reconstruction formula for bandlimited functions, through a sinc-type kernel, and a discrete Fourier transform from N samples properly chosen.  ...  of the pseudo-unitary group SU(1,1).  ...  Sánchez-Monreal, "Sampling Theorems and Discrete Fourier Transforms on Curved Phase Spaces of Constant Curvature: a Unified Treatment", in progress. de Matemática Aplicada y Estadística, Universidad Politécnica  ... 
doi:10.1007/s00041-010-9142-5 fatcat:t6po2uelubdlfnaunxmsmn73oq

Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics

Gerard 't Hooft
2021 Foundations of physics  
Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment.  ...  The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection.  ...  Acknowledgements The author benefited a lot from discussions with T. Palmer, F, Scardigli, C. Wetter-  ... 
doi:10.1007/s10701-021-00464-7 fatcat:3bv5uqmbkngkhi42hkziudvffi

Emergent Chiral Symmetry: Parity and Time Reversal Doubles

A. P. Balachandran, S. Vaidya
1997 International Journal of Modern Physics A  
A novel by-product of this mechanism is the emergence of an approximate symmetry (corresponding to the approximate degeneracy of the doubles) at low energies which is not evident in the full Hamiltonian  ...  In this article, we discuss the theoretical foundations of these doubles in detail, demonstrating their emergence as a surprisingly subtle consequence of the Born-Oppenheimer approximation, and emphasizing  ...  Acknowledgments We have discussed the contents of this article with several physicists. Special thanks are due to B. Dolan, M. V. N. Murthy, R.  ... 
doi:10.1142/s0217751x97002851 fatcat:vr6x4vlrsfgklcatlfs6rcrmu4

Time-dependent solution of the Liouville-von Neumann equation: non-dissipative evolution

Michael Berman, Ronnie Kosloff
1991 Computer Physics Communications  
The Fast Fourier Transform (FFT) is used to pass back and forth between coordinate and momentum representations, this transformation preserving all exact commutation relations.  ...  A typical non-trivial application is presented, namely, the splitting up of the probability density of a non-pure state into transmitted and reflected branches due to scattering off a potential barrier  ...  The transformation from coor-dinate to momentum representation is achieved by Once the numerical algorithm is checked, its discrete Fast Fourier Transform (FFT) [39] al-relation to analytic solutions  ... 
doi:10.1016/0010-4655(91)90233-b fatcat:hakevfg77jb5pkfhke4m6jn7iu

A note on the mean value of the zeta and L-functions. XIV [article]

Yoichi Motohashi
2004 arXiv   pre-print
The aim of the present note is to develop a study on the feasibility of a unified theory of mean values of automorphic L-functions, a desideratum in the field.  ...  This is an outcome of the investigation commenced with Part XII of this series, where a framework was laid on the basis of the theory of automorphic representations, and a general approach to the mean  ...  Bruggeman for his expert comments to an earlier version of the present note. We thank to M. Jutila and A. Ivić for their encouraging comments.  ... 
arXiv:math/0401085v1 fatcat:26cltrnvgfcnhlgnuymbbhstq4

Mini-Workshop: Shearlets

Gitta Kutyniok, Demetrio Labate
2010 Oberwolfach Reports  
Since its introduction about five years ago, the theory of shearlets has rapidly developed and gained wide recognition as the superior way of achieving a truly unified treatment in both the continuum and  ...  By now, shearlet analysis has reached maturity as a research field, with deep mathematical results, efficient numerical methods, and a variety of high-impact applications.  ...  structure, optimally sparse approximations of certain image classes, compactly supported generators, fast decomposition algorithms, and unified treatment of the continuum and digital realm.  ... 
doi:10.4171/owr/2010/44 fatcat:hkt2fklqnfgxnnfu2xyflihjm4

A Unitary Extension Principle for Shearlet Systems [article]

Bin Han, Gitta Kutyniok, Zuowei Shen
2009 arXiv   pre-print
In this paper, we first introduce the concept of an adaptive MRA (AMRA) structure which is a variant of the classical MRA structure suited to the main goal of a fast flexible decomposition strategy adapted  ...  We then study this novel methodology for the general case of affine-like systems, and derive a Unitary Extension Principle (UEP) for filter design.  ...  The facts that they provide a unified treatment in both the continuous as well as digital setting and that the digital setting admits a multiresolution analysis leading to a fast spatial domain decomposition  ... 
arXiv:0912.4529v1 fatcat:ukmec4nfsrbahnskhn5vsz7y5u

Quantum factoring, discrete logarithms, and the hidden subgroup problem

R. Jozsa
2001 Computing in science & engineering (Print)  
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms.  ...  In this article we review the essential ingredients of these algorithms and draw out the unifying generalization of the so-called abelian hidden subgroup problem.  ...  the essential ingredients appear to be implicit in the work of Kitaev [9] and Shor's treatment [7] of factoring and discrete logarithms).  ... 
doi:10.1109/5992.909000 fatcat:jeorlfkwdzfvxbjbwijenwscyq

Wavelet Transform on the Circle and the Real Line: A Unified Group-Theoretical Treatment [article]

Manuel Calixto, Julio Guerrero
2006 arXiv   pre-print
A general procedure for obtaining unitary representations of a group G of affine transformations on a space of signals L^2(X,dx) is described, relating carrier spaces X to (first or higher-order) "polarization  ...  We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle S^1 and the real line R, following the general formalism of Coherent States (CS) associated to  ...  It remains to study "the discrete approach", which roots in the Littlewood-Paley analysis, and yields fast algorithms for computing the wavelet transform numerically.  ... 
arXiv:math-ph/0406057v2 fatcat:v2mujgx7kvg3rphsepudckpbda

Wavelet transform on the circle and the real line: A unified group-theoretical treatment

M. Calixto, J. Guerrero
2006 Applied and Computational Harmonic Analysis  
A general procedure for obtaining unitary representations of a group G of affine transformations on a space of signals L 2 (X, dx) is described, relating carrier spaces X to (first-or higher-order) "polarization  ...  We present a unified group-theoretical derivation of the continuous wavelet transform (CWT) on the circle S 1 and the real line R, following the general formalism of coherent states (CS) associated to  ...  It remains to study "the discrete approach," which roots in the Littlewood-Paley analysis, and yields fast algorithms for computing the wavelet transform numerically.  ... 
doi:10.1016/j.acha.2006.02.001 fatcat:4vzwsiooercatbv7kjcaquueyy

A Brief Overview of Results about Uniqueness of the Quantization in Cosmology

Jerónimo Cortez, Guillermo A. Mena Marugán, José M. Velhinho
2021 Universe  
We discuss the extent to which a unitary implementation of the resulting group suffices to fix the quantization—a demand that can be seen as a weaker version of the requirement of invariance.  ...  These criteria impose certain conditions on the representation of a group of physically relevant linear transformations. Generally, this group contains any existing symmetry of the spatial sections.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/universe7080299 fatcat:fjstbhvw2fdmpiwzpzrgkrlzz4

Fast quantum algorithms for numerical integrals and stochastic processes [article]

Daniel S. Abrams, Colin P. Williams
1999 arXiv   pre-print
quite different) approaches can be understood from the same unified framework.  ...  We derive a simpler and slightly faster version of Grover's mean algorithm, demonstrate how to apply quantum counting to the problem, develop some variations of these algorithms, and show how both (apparently  ...  It is therefore a simple matter to create a superposition |Ψ >= 1 √ A A−1 j=0 |j G j |s (13) and determine the value of r by performing a fast Fourier transform on the first register.  ... 
arXiv:quant-ph/9908083v1 fatcat:ho2ppqtdojenbbcjpna3syyfqe
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