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仿射框架的新准则 被引量：1

A NEW CRITERION ON AFFINE FRAMES
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摘要 仿射框架是小波理论中很基本的概念.熟知的关于仿射框架的Daubechies判别法引用了由绝对值| (ajω) (ajω+lT)|算出的量来作判别.在本文建立的新判别法中引用了由(ajω) (ajω+lT)的适当组合的代数和算出的量来作判别.当为偶函数时,新的判别法优于Daubechies判别法. Affine frame is a very basic concept in wavelet theory. In the well-known Daubechies Criterion for affine frames the quantities which are calculated in terms of absolute values | (aJω) (aJω + lT)| are applied. In the new criterion established in this paper the authors use new criterion quantities which are calculated via algebric sums of suitable combinations of (ajω) (ajω + lT). When is an even function, the new criterion is more advanced than Daubechies criterion.
作者 施咸亮 石棋玲
机构地区 湖南师范大学数学与计算机科学学院
出处 《数学年刊（A辑）》 CSCD 北大核心 2005年第2期257-262,共6页 Chinese Annals of Mathematics
关键词 仿射框架 判别准则 Daubechies判别法 Affine frame, New criterion, Daubechies criterion
分类号 O174.2 [理学—基础数学]
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参考文献11

  • 1Chui, C. K., An Introduction to Wavelets [M], Academic Press, Boston, 1992.
  • 2Chui, C. K. & Shi, X. L., Inequalities of Littlewood-Paley type for frames and wavelets [J], SIAM J. Math. Anal., 24(1993), 263-277.
  • 3Chui, C. K. & Shi, X. L., Bessel sequences and affine frames [J], Appl. Comput. Harmon.Anal., 1(1993), 29-49.
  • 4Chui, C. K. & Shi, X. L., Characterization of biorthogonal cosine wavelets [J], J. of Fourier Anal. and Appl., 3:5(1997), 559-575.
  • 5Chui, C. K. & Shi, X. L., Wavelets of Wilson type with arbitrary shapes [J], Appl.Comput. Harmon. Anal., 8(2000), 1-23.
  • 6Chui, C. K. & Shi, X. L., Orthonormal wavelets and tight frames with arbitrary real dilations [J], Appl. Comput. Harmon. Anal., 9(2000), 243-264.
  • 7Daubechies, I., The wavelet transform, time-frequency localization and signal analysis [J], IEEE Trans. Inform. Theory, 36(1990), 961-1005.
  • 8Daubechies, I., Ten Lectures on Wavelets [M], CBMS-NSF Series in Applied Math.,Vol. 61, SIAM, Philadelphia, 1992.
  • 9Duffin, R. J. & A. C. Schaeffer, A class of nonharmonic Fourier series [J], Trans. Amer.Math. Soc., 72(1952), 341-366.
  • 10Kahane, J. & Lemarie-Rieusset, P. G., Fourier Series and Wavelets [M], Gordon and Breach Publishers, France, 1994.

同被引文献8

  • 1Daubechies I. The wavelet transform time-frequency localization and signal analysis. IEEE Trans Inform Theory, 1990, 36:961～1005
  • 2Chui C K, Shi X L. Inequalities of Littlewood-Paley type for frames and wavelets. SIAM J Math Anal,1993, 24:263～277
  • 3Chui C K. An Introduction to Wavelets. Boston: Academic Press, 1992
  • 4Daubechies I. Ten Lectures on Wavelets. CBMS-NSF Series in Applied Math, Vol 61. Philadelphia:SIAM, 1992
  • 5Kahane J, Lemarie'-Rieusset P G. Fourier Series and Wavelets. Paris: Gordon and Breach Publishers,1994
  • 6Kaiser G, Friendly A. Guide to Wavelets. Berlin, Boston: Birkhauser, 1994
  • 7Christensen O. An Introduction to Frames and Riese Bases. Boston: Birkhauser, 2002
  • 8Chui C K, Shi X L. Orthonormal wavelets and tight frames with arbitrary real dilations. Appl Comput Harmon Anal, 2000, 9:243～264

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数学年刊（A辑）
2005年 第2期

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