Generalized Fourier Transform for Non-Uniform Sampled Data

  • Krzysztof Kazimierczuk
  • Maria Misiak
  • Jan Stanek
  • Anna Zawadzka-Kazimierczuk
  • Wiktor Koźmiński
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 316)


Fourier transform can be effectively used for processing of sparsely sampled multidimensional data sets. It provides the possibility to acquire NMR spectra of ultra-high dimensionality and/or resolution which allow easy resonance assignment and precise determination of spectral parameters, e.g., coupling constants. In this chapter, the development and applications of non-uniform Fourier transform is presented.


Biomolecular NMR Multidimensional NMR Non-linear sampling Sparse sampling 



This work has been supported in part by the EC contract EAST-NMR no 228461. Bio-NMR project under the seventh Framework Programme of the EC grant agreement 261863 for conducting the research is gratefully acknowledged. A.Z.-K. thanks the Foundation for Polish Science for supporting her with the MPD Programme that was co-financed by the EU European Regional Development Fund. K.K. thanks the Foundation for Polish Science for supporting him with the KOLUMB scholarship. M.M. and W.K. acknowledge the Ministry of Science and Higher Education of Poland for the grant N204 137937 for the years 2009–2010. We are grateful to V. Motáčková, J. Nováček, L. Žídek, H. Šanderová, L. Krásný, and V. Sklenář for providing Fig. 18.


  1. 1.
    Ernst RR, Anderson WA (1966) Rev Sci Instrum 37:93CrossRefGoogle Scholar
  2. 2.
    Jeener J (1971) Basko Polje, YugoslaviaGoogle Scholar
  3. 3.
    Aue WP, Bartholdi E, Ernst RR (1976) J Chem Phys 64:2229CrossRefGoogle Scholar
  4. 4.
    Wüthrich K (1986) NMR of proteins and nucleic acids. Wiley, New YorkGoogle Scholar
  5. 5.
    Montelione GT, Wagner G (1989) J Am Chem Soc 111:5474CrossRefGoogle Scholar
  6. 6.
    Ikura M, Kay LE, Bax A (1990) Biochemistry 29:4659CrossRefGoogle Scholar
  7. 7.
    Bax A, Grzesiek S (1993) Acc Chem Res 26:131CrossRefGoogle Scholar
  8. 8.
    Yamazaki T, Lee W, Arrowsmith CH, Muhandiram DR, Kay LE (1994) J Am Chem Soc 116:11655CrossRefGoogle Scholar
  9. 9.
    Sattler M, Schleucher J, Griesinger C (1999) Prog Nucl Magn Reson Spectrosc 34:93CrossRefGoogle Scholar
  10. 10.
    Moskau D (2002) Concepts Magn Reson 15:164CrossRefGoogle Scholar
  11. 11.
    Szantay C (2008) Concepts Magn Reson Part A 32A:373CrossRefGoogle Scholar
  12. 12.
    Schanda P, Kupče Ē, Brutscher B (2005) J Biomol NMR 33:199CrossRefGoogle Scholar
  13. 13.
    Schanda P, Van Melckebeke H, Brutscher B (2006) J Am Chem Soc 128:9042CrossRefGoogle Scholar
  14. 14.
    Lescop E, Schanda P, Brutscher B (2007) J Magn Reson 187:163CrossRefGoogle Scholar
  15. 15.
    Frydman L, Scherf T, Lupulescu A (2002) Proc Natl Acad Sci USA 99:15858CrossRefGoogle Scholar
  16. 16.
    Mishkovsky M, Frydman L (2008) Chemphyschem 9:2340CrossRefGoogle Scholar
  17. 17.
    Mishkovsky M, Kupče Ē, Frydman L (2007) J Chem Phys 127:034507CrossRefGoogle Scholar
  18. 18.
    Gal M, Frydman L (2010) J Magn Reson 203:311CrossRefGoogle Scholar
  19. 19.
    Mishkovsky M, Frydman L (2009) Annu Rev Phys Chem 60:429CrossRefGoogle Scholar
  20. 20.
    Tal A, Frydman L (2010) Prog Nucl Magn Reson Spectrosc 57:241CrossRefGoogle Scholar
  21. 21.
    Led JJ, Gesmar H (2010) In: Morris GA, Emsley JW (eds) Multidimensional NMR methods for the solution state. Wiley, Chichester, p 131Google Scholar
  22. 22.
    Armstrong GS, Cano KE, Mandelshtam VA, Shaka AJ, Bendiak B (2004) J Magn Reson 170:156CrossRefGoogle Scholar
  23. 23.
    Armstrong GS, Mandelshtam VA, Shaka AJ, Bendiak B (2005) J Magn Reson 173:160CrossRefGoogle Scholar
  24. 24.
    Meng X, Nguyen BD, Ridge C, Shaka AJ (2009) J Magn Reson 196:12CrossRefGoogle Scholar
  25. 25.
    Brüschweiler R (2004) J Chem Phys 121:409CrossRefGoogle Scholar
  26. 26.
    Brüschweiler R, Zhang FL (2004) J Chem Phys 120:5253CrossRefGoogle Scholar
  27. 27.
    Snyder DA, Bruschweiler R (2009) J Phys Chem A 113:12898CrossRefGoogle Scholar
  28. 28.
    Snyder DA, Xu Y, Yang D, Bruschweiler R (2007) J Am Chem Soc 129:14126CrossRefGoogle Scholar
  29. 29.
    Trbovic N, Smirnov S, Zhang F, Bruschweiler R (2004) J Magn Reson 171:277CrossRefGoogle Scholar
  30. 30.
    Zhang FL, Bruschweiler R (2004) J Am Chem Soc 126:13180CrossRefGoogle Scholar
  31. 31.
    Robin M, Delsuc M-A, Guittet E, Lallemand J-Y (1991) J Magn Reson 92:645Google Scholar
  32. 32.
    Jeannerat D (2007) J Magn Reson 186:112CrossRefGoogle Scholar
  33. 33.
    Coggins BE, Venters RA, Zhou P (2010) Prog Nucl Magn Reson Spectrosc 57:381CrossRefGoogle Scholar
  34. 34.
    Kazimierczuk K, Stanek J, Zawadzka-Kazimierczuk A, Koźmiński W (2010) Prog Nucl Magn Reson Spectrosc 57:420CrossRefGoogle Scholar
  35. 35.
    Kim S, Szyperski T (2003) J Am Chem Soc 125:1385CrossRefGoogle Scholar
  36. 36.
    Ding KY, Gronenborn AM (2002) J Magn Reson 156:262CrossRefGoogle Scholar
  37. 37.
    Koźmiński W, Zhukov I (2003) J Biomol NMR 26:157CrossRefGoogle Scholar
  38. 38.
    Hiller S, Fiorito F, Wüthrich K, Wider G (2005) Proc Natl Acad Sci USA 102:10876CrossRefGoogle Scholar
  39. 39.
    Malmodin D, Billeter M (2005) J Magn Reson 176:47CrossRefGoogle Scholar
  40. 40.
    Kupče Ē, Freeman R (2005) J Magn Reson 173:317CrossRefGoogle Scholar
  41. 41.
    Kupče Ē, Freeman R (2003) J Am Chem Soc 125:13958CrossRefGoogle Scholar
  42. 42.
    Kupče Ē, Freeman R (2004) Concepts Magn Reson Part A 22A:4CrossRefGoogle Scholar
  43. 43.
    Kupče Ē, Freeman R (2004) J Biomol NMR 28:391CrossRefGoogle Scholar
  44. 44.
    Kazimierczuk K, Koźmiński W, Zhukov I (2006) J Magn Reson 179:323CrossRefGoogle Scholar
  45. 45.
    Kazimierczuk K, Zawadzka A, Koźmiński W (2009) J Magn Reson 197:219CrossRefGoogle Scholar
  46. 46.
    Kazimierczuk K, Zawadzka A, Koźmiński W, Zhukov I (2006) J Biomol NMR 36:157CrossRefGoogle Scholar
  47. 47.
    Laue ED, Skilling J, Staunton J, Sibisi S, Brereton RG (1985) J Magn Reson 62:437Google Scholar
  48. 48.
    Hoch JC, Stern AS (1996) NMR data processing. Wiley-Interscience, New YorkGoogle Scholar
  49. 49.
    Mobli M, Hoch JC (2008) Concepts Magn Reson Part A 32A:436CrossRefGoogle Scholar
  50. 50.
    Luan T, Jaravine V, Yee A, Arrowsmith CH, Orekhov VY (2005) J Biomol NMR 33:1CrossRefGoogle Scholar
  51. 51.
    Jaravine V, Ibraghimov I, Orekhov VY (2006) Nat Meth 3:605CrossRefGoogle Scholar
  52. 52.
    Jaravine VA, Zhuravleva AV, Permi P, Ibraghimov I, Orekhov VY (2008) J Am Chem Soc 130:3927CrossRefGoogle Scholar
  53. 53.
    Szantay C (2008) Concepts Magn Reson Part A 32A:1CrossRefGoogle Scholar
  54. 54.
    Nyquist H (2002) Proc IEEE 90:280CrossRefGoogle Scholar
  55. 55.
    Marion D (2006) J Biomol NMR 36:45CrossRefGoogle Scholar
  56. 56.
    Coggins BE, Zhou P (2006) J Magn Reson 182:84CrossRefGoogle Scholar
  57. 57.
    Szyperski T, Yeh DC, Sukumaran DK, Moseley HN, Montelione GT (2002) Proc Natl Acad Sci USA 99:8009CrossRefGoogle Scholar
  58. 58.
    Malmodin D, Billeter M (2006) Magn Reson Chem 44:185CrossRefGoogle Scholar
  59. 59.
    Coggins BE, Zhou P (2007) J Magn Reson 184:207CrossRefGoogle Scholar
  60. 60.
    Kazimierczuk K, Zawadzka A, Koźmiński W, Zhukov I (2007) J Magn Reson 188:344CrossRefGoogle Scholar
  61. 61.
    Kazimierczuk K, Zawadzka A, Koźmiński W (2008) J Magn Reson 192:123CrossRefGoogle Scholar
  62. 62.
    Hyberts SG, Takeuchi K, Wagner G (2010) J Am Chem Soc 132:2145CrossRefGoogle Scholar
  63. 63.
    Tarczynski A, Allay N (2003) 7th world multiconference on systemics, Cybernetics and Informatics, Proceedings, Vol IV, p 344Google Scholar
  64. 64.
    Pannetier N, Houben K, Blanchard L, Marion D (2007) J Magn Reson 186:142CrossRefGoogle Scholar
  65. 65.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes: the art of scientific computing. Cambridge University Press, Cambridge/New YorkGoogle Scholar
  66. 66.
    Davis PJ, Rabinowitz P (1984) Methods of numerical integration. Academic, New YorkGoogle Scholar
  67. 67.
    Barthold E, Ernst RR (1973) J Magn Reson 11:9Google Scholar
  68. 68.
    Hoch JC, Stern AS, Wagner G (1995) J Cell Biochem, Suppl. 21B: 76Google Scholar
  69. 69.
    Matsuki Y, Eddy MT, Herzfeld J (2009) J Am Chem Soc 131:4648CrossRefGoogle Scholar
  70. 70.
    Donoho DL (2006) Commun Pure Appl Math 59:797CrossRefGoogle Scholar
  71. 71.
    Lustig M, Donoho D, Pauly JM (2007) Magn Reson Med 58:1182CrossRefGoogle Scholar
  72. 72.
    Lustig M, Donoho DL, Santos JM, Pauly JM (2008) IEEE Signal Process Mag 25:72CrossRefGoogle Scholar
  73. 73.
    Drori I (2007) Eurasip J Adv Signal Process doi:10.1155/2007/20248Google Scholar
  74. 74.
    Shrot Y, Frydman L (2011) J Magn Reson 209:352Google Scholar
  75. 75.
    Hyberts SG, Frueh DP, Arthanari H, Wagner G (2009) J Biomol NMR 45:283CrossRefGoogle Scholar
  76. 76.
    Stern AS, Donoho DL, Hoch JC (2007) J Magn Reson 188:295CrossRefGoogle Scholar
  77. 77.
    Marion D (2005) J Biomol NMR 32:141CrossRefGoogle Scholar
  78. 78.
    Jiang B, Jiang X, Xiao N, Zhang X, Jiang L, Mao XA, Liu M (2010) J Magn Reson 204:165CrossRefGoogle Scholar
  79. 79.
    Kazimierczuk K, Zawadzka A, Koźmiński W, Zhukov I (2008) J Am Chem Soc 130:5404CrossRefGoogle Scholar
  80. 80.
    Kazimierczuk K, Zawadzka-Kazimierczuk A, Koźmiński W (2010) J Magn Reson 205:286CrossRefGoogle Scholar
  81. 81.
    Zawadzka-Kazimierczuk A, Kazimierczuk K, Koźmiński W (2010) J Magn Reson 202:109CrossRefGoogle Scholar
  82. 82.
    Coggins BE, Venters RA, Zhou P (2004) J Am Chem Soc 126:1000CrossRefGoogle Scholar
  83. 83.
    Coggins BE, Zhou P (2008) J Biomol NMR 42:225CrossRefGoogle Scholar
  84. 84.
    Werner-Allen JW, Coggins BE, Zhou P (2010) J Magn Reson 204:173CrossRefGoogle Scholar
  85. 85.
    Stanek J, Koźmiński W (2010) J Biomol NMR 47:65CrossRefGoogle Scholar
  86. 86.
    Högbom JA (1974) Astron Astrophys Suppl Ser 15:417Google Scholar
  87. 87.
    Keeler J (1984) J Magn Reson 56:463Google Scholar
  88. 88.
    Shaka AJ, Keeler J, Freeman R (1984) J Magn Reson 56:294Google Scholar
  89. 89.
    Barna JCJ, Tan SM, Laue ED (1988) J Magn Reson 78:327Google Scholar
  90. 90.
    Barna JCJ, Laue ED, Mayger MR, Skilling J, Worrall SJP (1987) J Magn Reson 73:69Google Scholar
  91. 91.
    Davies SJ, Bauer C, Hore PJ, Freeman R (1988) J Magn Reson 76:476Google Scholar
  92. 92.
    Motáčková V, Nováček J, Zawadzka-Kazimierczuk A, Kazimierczuk K, Žídek L, Šanderová H, Krásný L, Koźmiński W, Sklenář V (2010) J Biomol NMR 48:169CrossRefGoogle Scholar
  93. 93.
    Eberstadt M, Gemmecker G, Mierke DF, Kessler H (1995) Angew Chem Int Ed Engl 34:1671CrossRefGoogle Scholar
  94. 94.
    Griesinger C, Sorensen OW, Ernst RR (1985) J Am Chem Soc 107:6394CrossRefGoogle Scholar
  95. 95.
    Misiak M, Koźmiński W (2007) Magn Reson Chem 45:171CrossRefGoogle Scholar
  96. 96.
    Misiak M, Koźmiński W, Kwasiborska M, Wójcik J, Ciepichal E, Swiezewska E (2009) Magn Reson Chem 47:825CrossRefGoogle Scholar
  97. 97.
    Meier S, Benie AJ, Duus JO, Sorensen OW (2009) J Magn Reson 200:340CrossRefGoogle Scholar
  98. 98.
    Meier S, Petersen BO, Duus JO, Sorensen OW (2009) Carbohydr Res 344:2274CrossRefGoogle Scholar
  99. 99.
    Findeisen M, Bermel W, Berger S (2006) Magn Reson Chem 44:455CrossRefGoogle Scholar
  100. 100.
    Misiak M, Koźmiński W (2009) Magn Reson Chem 47:205CrossRefGoogle Scholar
  101. 101.
    Ludwig C, Marin-Montesinos I, Saunders MG, Gunther UL (2010) J Am Chem Soc 132:2508CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Krzysztof Kazimierczuk
    • 1
    • 2
  • Maria Misiak
    • 1
  • Jan Stanek
    • 1
  • Anna Zawadzka-Kazimierczuk
    • 1
  • Wiktor Koźmiński
    • 1
  1. 1.Faculty of ChemistryUniversity of WarsawWarsawPoland
  2. 2.Swedish NMR CentreUniversity of GothenburgGothenburgSweden

Personalised recommendations