메뉴 건너뛰기




Volumn 20, Issue 2, 2010, Pages 271-284

Directional uncertainty principle for quaternion fourier transform

Author keywords

Geometric algebra; Multivector wave packets; Quaternions; Spacetime algebra; Uncertainty

Indexed keywords


EID: 77952321667     PISSN: 01887009     EISSN: 16614909     Source Type: Journal    
DOI: 10.1007/s00006-009-0175-2     Document Type: Article
Times cited : (100)

References (32)
  • 1
    • 0027810912 scopus 로고
    • Quaternionic-Fourier Transform for Analysis of Two-dimensional Lin-ear Time-Invariant Partial Differential Systems
    • T. A. Ell, Quaternionic-Fourier Transform for Analysis of Two-dimensional Lin-ear Time-Invariant Partial Differential Systems. In Proceedings of the 32nd IEEE Conference on Decision and Control, December 15-17, 2 (1993), 1830-1841.
    • (1993) Proceedings of The 32nd IEEE Conference On Decision and Control, December , vol.15-17 , Issue.2 , pp. 1830-1841
    • Ell, T.A.1
  • 2
    • 34548099156 scopus 로고    scopus 로고
    • Quaternion Fourier Transform on Quaternion Fields and Generalizations
    • E. Hitzer, Quaternion Fourier Transform on Quaternion Fields and Generalizations. Adv. Appl. Cliff. Alg. 17 (3) (2007), 497-517.
    • (2007) Adv. Appl. Cliff. Alg , vol.17 , Issue.3 , pp. 497-517
    • Hitzer, E.1
  • 6
    • 77952321062 scopus 로고    scopus 로고
    • Real Quaternionic Calculus Handbook
    • May
    • S. Georgiev, Real Quaternionic Calculus Handbook. Private communication, May 2009.
    • (2009) Private Communication
    • Georgiev, S.1
  • 7
    • 33748945587 scopus 로고    scopus 로고
    • Clifford Fourier Transform and Uncertainty Principle for the Clifford Geometric Algebra Cl3,0
    • B. Mawardi and E. Hitzer, Clifford Fourier Transform and Uncertainty Principle for the Clifford Geometric Algebra Cl3,0. Adv. Appl. Cliff. Alg. 16 (1) (2006), 41-61.
    • (2006) Adv. Appl. Cliff. Alg , vol.16 , Issue.1 , pp. 41-61
    • Mawardi, B.1    Hitzer, E.2
  • 8
    • 58149489140 scopus 로고    scopus 로고
    • Clifford Fourier Transform on Multivector Fields and Uncertainty Principle for Dimensions n = 2 (mod 4) and n = 3 (mod 4)
    • P. Anglès (ed.)
    • E. Hitzer and B. Mawardi, Clifford Fourier Transform on Multivector Fields and Uncertainty Principle for Dimensions n = 2 (mod 4) and n = 3 (mod 4). P. Anglès (ed.), Adv. Appl. Cliff. Alg. 18 S3,4 (2008), 715-736.
    • (2008) Adv. Appl. Cliff. Alg , vol.18 , Issue.4 , pp. 715-736
    • Hitzer, E.1    Mawardi, B.2
  • 9
    • 0003604708 scopus 로고
    • Vol. 76 of Research Notes in Mathematics, Pitman Advanced Publishing Program
    • F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis. Vol. 76 of Research Notes in Mathematics, Pitman Advanced Publishing Program, 1982.
    • (1982) Clifford Analysis
    • Brackx, F.1    Delanghe, R.2    Sommen, F.3
  • 11
    • 0000570087 scopus 로고
    • Clifford Algebras, Fourier Transform and Singular Convolution Operators On Lipschitz Surfaces
    • C. Li, A. McIntosh and T. Qian, Clifford Algebras, Fourier Transform and Singular Convolution Operators On Lipschitz Surfaces. Revista Matematica Iberoamericana 10(3)(1994),665-695.
    • (1994) Revista Matematica Iberoamericana , vol.10 , Issue.3 , pp. 665-695
    • Li, C.1    McIntosh, A.2    Qian, T.3
  • 12
    • 0001927753 scopus 로고    scopus 로고
    • Clifford Algebras, Fourier Theory, Singular Integrals, and Harmonic Functions on Lipschitz Domains
    • Chapter 1 of J. Ryan (ed.), CRC Press, Boca Raton
    • A. McIntosh, Clifford Algebras, Fourier Theory, Singular Integrals, and Harmonic Functions on Lipschitz Domains. Chapter 1 of J. Ryan (ed.), Clifford Algebras in Analysis and Related Topics, CRC Press, Boca Raton, 1996.
    • (1996) Clifford Algebras In Analysis and Related Topics
    • McIntosh, A.1
  • 13
    • 34548103510 scopus 로고    scopus 로고
    • Paley-Wiener Theorems and Shannon Sampling in the Clifford Analysis Setting
    • In R. Ablamowicz (ed.), Physics, and Engineering, Birkäuser, Basel
    • T. Qian, Paley-Wiener Theorems and Shannon Sampling in the Clifford Analysis Setting. In R. Ablamowicz (ed.), Clifford Algebras - Applications to Mathematics, Physics, and Engineering, Birkäuser, Basel, (2004), 115-124.
    • (2004) Clifford Algebras - Applications to Mathematics , pp. 115-124
    • Qian, T.1
  • 15
    • 84957696217 scopus 로고    scopus 로고
    • Uncertainty Principle for the Clifford Geometric Algebra Cln,0, n = 3(mod 4) based on Clifford Fourier transform
    • E. Hitzer and B. Mawardi, Uncertainty Principle for the Clifford Geometric Algebra Cln,0, n = 3(mod 4) based on Clifford Fourier transform. In Springer SCI book series Applied and Numerical Harmonic Analysis 2006, pp. 45-54.
    • (2006) In Springer SCI Book Series Applied and Numerical Harmonic Analysis , pp. 45-54
    • Hitzer, E.1    Mawardi, B.2
  • 17
    • 0035503273 scopus 로고    scopus 로고
    • Efficient Implementation of Quat. Fourier Transf., Convolution and Correlation by 2-D Complex FFT
    • S. C. Pei, J. J. Ding and J. H. Chang, Efficient Implementation of Quat. Fourier Transf., Convolution and Correlation by 2-D Complex FFT. IEEE Trans. on Sig. Proc. 49 (11) (2001), 2783-2797.
    • (2001) IEEE Trans. On Sig. Proc , vol.49 , Issue.11 , pp. 2783-2797
    • Pei, S.C.1    Ding, J.J.2    Chang, J.H.3
  • 18
    • 33748947533 scopus 로고    scopus 로고
    • An Introduction to Commutative Quaternions
    • F. Catoni, R. Cannata and P. Zampetti, An Introduction to Commutative Quaternions. Adv. Appl. Cliff. Alg. 16 (1) (2006), 1-28.
    • (2006) Adv. Appl. Cliff. Alg , vol.16 , Issue.1 , pp. 1-28
    • Catoni, F.1    Cannata, R.2    Zampetti, P.3
  • 19
    • 15944389562 scopus 로고    scopus 로고
    • On The Heisenberg-Weyl Inequality
    • J. M. Rassias, On The Heisenberg-Weyl Inequality. Jour. of Inequalities in Pure and Appl. Math., 6 (1), article 11, (2005), 1-18. http://www.primedu.uoa.gr/jrasssias/
    • (2005) Jour. of Inequalities In Pure and Appl. Math , vol.6 , Issue.article 11 , pp. 1-18
    • Rassias, J.M.1
  • 29
    • 77952322626 scopus 로고    scopus 로고
    • Quaternions, algèbre de Clifford et physique relativiste. Presses polytechniques, et universitaires romandes, 2004 (French)
    • Birkhäuser, Basel, (English)
    • P. Girard, Quaternions, algèbre de Clifford et physique relativiste. Presses polytechniques, et universitaires romandes, 2004 (French); Quaternions, Clifford Algebras and Relativistic Physics. Birkhäuser, Basel, 2007 (English).
    • (2007) Quaternions, Clifford Algebras and Relativistic Physics
    • Girard, P.1
  • 30
    • 84882218552 scopus 로고    scopus 로고
    • Geometric Algebra for Computer Science: An Object-oriented Approach to Geometry
    • Elsevier, San Francisco
    • L. Dorst, D. Fontijne and S. Mann, Geometric Algebra for Computer Science: An Object-oriented Approach to Geometry. Morgan Kaufmann Series in Computer Graphics, Elsevier, San Francisco, 2007.
    • (2007) Morgan Kaufmann Series In Computer Graphics
    • Dorst, L.1    Fontijne, D.2    Mann, S.3
  • 31
    • 85032069041 scopus 로고    scopus 로고
    • Invariant algebras and geometric reasoning
    • Singapore
    • H. Li, Invariant algebras and geometric reasoning. World Scientific, Singapore, 2008.
    • (2008) World Scientific
    • Li, H.1
  • 32
    • 77952320601 scopus 로고    scopus 로고
    • Director of the US National Human Genome Research Institute
    • 5 Nov
    • F. Collins, Director of the US National Human Genome Research Institute, in Time Magazine, 5 Nov. 2006.
    • (2006) Time Magazine
    • Collins, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.