rbioinfo.m
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波变换

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Matlab

  1. function rbioinfo
  2. %RBIOINFO Information on reverse biorthogonal spline wavelets.
  3. %
  4. %   Reverse Biorthogonal Wavelets
  5. %
  6. %   General characteristics: Compactly supported 
  7. %   biorthogonal spline wavelets for which 
  8. %   symmetry and exact reconstruction are possible
  9. %   with FIR filters (in orthogonal case it is 
  10. %   impossible except for Haar).
  11. %
  12. %   Family                  Biorthogonal
  13. %   Short name              rbio
  14. %   Order Nd,Nr             Nd = 1 , Nr = 1, 3, 5
  15. %   r for reconstruction    Nd = 2 , Nr = 2, 4, 6, 8
  16. %   d for decomposition     Nd = 3 , Nr = 1, 3, 5, 7, 9
  17. %                           Nd = 4 , Nr = 4
  18. %                           Nd = 5 , Nr = 5
  19. %                           Nd = 6 , Nr = 8
  20. %
  21. %   Examples                rbio3.1, rbio5.5
  22. %
  23. %   Orthogonal              no
  24. %   Biorthogonal            yes
  25. %   Compact support         yes
  26. %   DWT                     possible
  27. %   CWT                     possible
  28. %
  29. %   Support width           2Nd+1 for rec., 2Nr+1 for dec.
  30. %   Filters length          max(2Nd,2Nr)+2 but essentially
  31. %   rbio Nd.Nr              lr                      ld
  32. %                     effective length        effective length
  33. %                       of Hi_D                  of Lo_D
  34. %
  35. %   rbio 1.1                 2                       2
  36. %   rbio 1.3                 6                       2
  37. %   rbio 1.5                10                       2
  38. %   rbio 2.2                 5                       3
  39. %   rbio 2.4                 9                       3
  40. %   rbio 2.6                13                       3
  41. %   rbio 2.8                17                       3
  42. %   rbio 3.1                 4                       4
  43. %   rbio 3.3                 8                       4
  44. %   rbio 3.5                12                       4
  45. %   rbio 3.7                16                       4
  46. %   rbio 3.9                20                       4
  47. %   rbio 4.4                 9                       7
  48. %   rbio 5.5                 9                      11
  49. %   rbio 6.8                17                      11
  50. %
  51. %   Regularity for          
  52. %   psi rec.                Nd-1 and Nd-2 at the knots
  53. %   Symmetry                yes  
  54. %   Number of vanishing 
  55. %   moments for psi dec.    Nd
  56. %
  57. %   Remark: rbio 4.4 , 5.5 and 6.8 are such that reconstruction and 
  58. %   decomposition functions and filters are close in value.           
  59. %
  60. %   Reference: I. Daubechies, 
  61. %   Ten lectures on wavelets, 
  62. %   CBMS, SIAM, 61, 1994, 271-280.
  63. %
  64. %   See Information on biorthogonal spline wavelets.   
  65. %   M. Misiti, Y. Misiti, G. Oppenheim, J.M. Poggi 12-Mar-1998.
  66. %   Last Revision: 09-Nov-2001.
  67. %   Copyright 1995-2002 The MathWorks, Inc.
  68. %   $Revision: 1.10 $  $Date: 2002/04/14 19:37:37 $