Application of Wavelet Transforms to Experimental Spectra: Smoothing, Denoising, and Data Set Compression

Analytical Chemistry

Volumn 69, Issue 1, 1997, Pages 78-90

  Barclay, V J ^a   Bonner, R F ^a   Hamilton, I P ^b  

^a MDS SCIEX   (Canada)

^b WILFRID LAURIER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1542712026     PISSN: 00032700     EISSN: None     Source Type: Journal    
DOI: 10.1021/ac960638m     Document Type: Article

References (27)

1. Erickson, C. L.; Lysaght, M. J.; Callis, J. B. Anal. Chem. 1992, 64, 1155A-1163A.
2. See, for example: Bialkowski, S. E. Anal. Chem. 1988, 60, 355A-361A, 403A-413A.
3. Barclay, V. J.; Bonner, R. F.; Hamilton, I. P.; Thibault, P., in preparation.
4. Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36, 1627-1639.
5. Tukey, J. W. Exploratory data analysis; Addison-Wesley: Reading, MA, 1977.
6. Stone, D. C. Can. J. Chem. 1995, 73, 1573-1581.
7. Ivaldi, J. C.; Tracy, D.; Barnard, T. W.; Slavin, W. Spectrochim. Acta 1992, 47B, 1361-1371.
8. Donoho, D. L.; Johnstone, I. M. Biometrika 1994, 81, 425-455.
9. Donoho, D. L.; Johnstone, I. M. Compt. Rend. Acad. Sci. Paris A 1994, 329, 1317-1322. Donoho, D. L.; Johnstone, I. M.; Kerkyacharian, G.; Picard, D. Journ. R. Stat. Soc. Ser B 1995, 57, 301-369. Donoho, D. L.; Buckheit J. In Wavelets in Statistics; Antoniadis, A., Oppenheim, G., Eds.; Springer-Verlag: New York, 1995.
10. Donoho, D. L.; Johnstone, I. M. Compt. Rend. Acad. Sci. Paris A 1994, 329, 1317-1322. Donoho, D. L.; Johnstone, I. M.; Kerkyacharian, G.; Picard, D. Journ. R. Stat. Soc. Ser B 1995, 57, 301-369. Donoho, D. L.; Buckheit J. In Wavelets in Statistics; Antoniadis, A., Oppenheim, G., Eds.; Springer-Verlag: New York, 1995.
11. Donoho, D. L.; Johnstone, I. M. Compt. Rend. Acad. Sci. Paris A 1994, 329, 1317-1322. Donoho, D. L.; Johnstone, I. M.; Kerkyacharian, G.; Picard, D. Journ. R. Stat. Soc. Ser B 1995, 57, 301-369. Donoho, D. L.; Buckheit J. In Wavelets in Statistics; Antoniadis, A., Oppenheim, G., Eds.; Springer-Verlag: New York, 1995.
12. Walczak, B.; van den Bogaert, B.; Massart, D. L. Anal. Chem. 1996, 68, 1742-1747. Note their convention for numbering of details is opposite to that employed here.
13. Daubechies, I. Ten Lectures on Wavelets; SIAM: Philadelphia, PA, 1992.
14. Meyer, Y. Wavelets: Algorithms and Applications; SIAM: Philadelphia, PA, 1993.
15. Chui, C. K. An Introduction to Wavelets; Academic Press: New York, 1992.
16. Kaiser, G. A Friendly Guide to Wavelets; Birkhäuser Boston, MA, 1994.
17. Bromba, M. U. A.; Ziegler, H. Anal. Chem. 1981, 53, 1583-1586.
18. Ziegler, H. Appl. Spectrosc. 1981, 35, 88-92.
19. Igor Pro 2.0, Wavemetrics, Oswego, OR, 1994.
20. Haykin, S. Modern Filters; MacMillan: New York, 1989.
21. Hamming, R. W. Digital Filters, 3rd ed.; Prentice-Hall: Englewood Cliffs, NJ, 1989.
22. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1992.
23. Programs for Digital Signal Processing; IEEE Press: Piscataway, NJ, 1979. (See section 1.4 on Mixed Radix Fast Fourier Transforms.)
24. See, for example: WavBox by C. Taswell or WaveLab by D. Donoho; both appear to utilize Matlab. WaveMetrics has introduced this operation to Igor Pro 3.
25. We distinguish "compact", referring to the extent along the x-axis, from "compressed", referring to the ability to describe a signal with fewer basis functions than it requires in the raw form.
26. Covey, T. R.; Bonner, R. F.; Shushan, B. I.; Henion, J. Rapid Commun. Mass Spectrom. 1988, 2, 249-255.
27. Brigham, E. O. The Fast Fourier Transform, Prentice-Hall: Englewood Cliffs, NJ, 1974.