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7 - Mathematical transformations

Published online by Cambridge University Press:  05 June 2012

William A. Pearlman
Affiliation:
Rensselaer Polytechnic Institute, New York
Amir Said
Affiliation:
Hewlett-Packard Laboratories, Palo Alto, California
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Digital Signal Compression
Principles and Practice
, pp. 166 - 217
Publisher: Cambridge University Press
Print publication year: 2011

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References

1. Fuller, W. A., Introduction to Statistical Time Series, 2nd edn. New York, NY: John Wiley & Sons. 1996.Google Scholar
2. Pearl, J., “On coding and filtering stationary signals by discrete Fourier transforms,” IEEE Trans. Inf. Theory, vol. 19, no. 2, pp. 229–232, Mar. 1973.CrossRefGoogle Scholar
3. Pearlman, W. A., “A limit on optimum performance degradation in fixed-rate coding of the discrete Fourier transform,” IEEE Trans. Inf. Theory, vol. 22, no. 4, pp. 485–488, Jul. 1976.CrossRefGoogle Scholar
4. Yemini, Y. and Pearl, J., “Asymptotic properties of discrete unitary transforms,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 1, no. 4, pp. 366–371, Oct. 1979.CrossRefGoogle ScholarPubMed
5. Ahmed, N., Natarajan, T. R., and Rao, K. R., “Discrete cosine transform,” IEEE Trans. Comput., vol. 23, no. 1, pp. 90–93, Jan. 1974.CrossRefGoogle Scholar
6. Narasimha, M. J. and Peterson, A. M., “On the computation of the discrete cosine transform,” IEEE Trans. Commun., vol. 26, no. 6, pp. 934–936, Jun. 1978.CrossRefGoogle Scholar
7. Malvar, H. S., Signal Processing with Lapped Transforms. Norwood, MA: Artech House. 1992.Google Scholar
8. Taubman, D. S. and Marcellin, M. W., JPEG2000: Image Compression Fundamentals, Standards, and Practice. Norwell, MA: Kluwer Academic Publishers. 2002.CrossRefGoogle Scholar
9. Cohen, A., Daubechies, I., and Feauveau, J.-C., “Biorthogonal bases of compactly supported wavelets,” Commun. Pure Appl. Math., vol. 45, no. 5, pp. 485–560, Jun. 1992.CrossRefGoogle Scholar
10. Vetterli, M. and Kovačević, J., Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice Hall. 1995.Google Scholar
11. Rao, R. M. and Bopardikar, A. S., Wavelet Transforms: Introduction to Theory and Applications. Reading, MA: Addison-Wesley Publishing Co., 1998.Google Scholar
12. Strang, G. and Nguyen, T., Wavelets and Filter Banks. Wellesley, MA: Wellesley-Cambridge Press. 1997.Google Scholar
13. Sweldens, W., “The lifting scheme: a custom-design construction of biorthogonal wavelets,” Appl. Comput. Harmon. Anal., vol. 3, no. 2, pp. 186–200, Apr. 1996.CrossRefGoogle Scholar
14. Said, A. and Pearlman, W. A., “An image multiresolution representation for lossless and lossy compression,” IEEE Trans. Image Process., vol. 5, no. 9, pp. 1303–1310, Sept. 1996.CrossRefGoogle ScholarPubMed
15. Zandi, A., Allen, J., Schwartz, E. L., and Boliek, M., “CREW: compression with reversible embedded wavelets,” in Proceedings of the IEEE Data Compression Conference, Snowbird, UT, Mar. 1995, pp. 212–221.Google Scholar
16. Calderbank, A. R., Daubechies, I., Sweldens, W., and Yeo, B.-L., “Wavelet transforms that map integers to integers,” Applied and Computational Harmonic Analysis, vol. 5, no. 3, pp. 332–369, Jul. 1998.CrossRefGoogle Scholar
17. Pratt, W. K., Digital Image Processing, 2nd edn. New York: J. Wiley & Sons, Inc., 1991.Google Scholar
18. Akansu, A. N. and Haddad, R. A., Multidimensional Signal Decomposition: Transforms, Subbands, and Wavelets, 2nd edn. San Diego, CA: Academic Press (Elsevier), 2001.Google Scholar
19. Crochiere, R. E. and Rabiner, L. R., Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1983.Google Scholar
Akansu, A. N. and Wadas, F. E., “On lapped orthogonal transform,” IEEE Trans. Signal Process., vol. 40, no. 2, pp. 439–442, Feb. 1992.CrossRefGoogle Scholar
Bellman, R., Introduction to Matrix Analysis, 2nd edn. New York, NY: McGraw-Hill Publishing Co., 1970.Google Scholar
Diniz, P. S. R., Silva, E. A. B., and Netto, S. L., Digital Signal Processing. Cambridge, England: Cambridge University Press. 2002.
Jayant, N. S. and Noll, P., Digital Coding of Waveforms. Englewood Cliffs, NJ: Prentice Hall. 1984.Google Scholar
Pearlman, W. A., “Performance bounds for subband coding,” in Subband Image Coding, Woods, J. W., edn. Norwell, MA: Kluwer Academic Publishers. 1991, ch. 1.Google Scholar
Sweldens, W., “The lifting scheme: a construction of second generation wavelets,” SIAM J. Math. Anal., vol. 29, no. 2, pp. 511–546, Mar. 1998.CrossRefGoogle Scholar

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  • Mathematical transformations
  • William A. Pearlman, Rensselaer Polytechnic Institute, New York, Amir Said, Hewlett-Packard Laboratories, Palo Alto, California
  • Book: Digital Signal Compression
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511984655.008
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  • Mathematical transformations
  • William A. Pearlman, Rensselaer Polytechnic Institute, New York, Amir Said, Hewlett-Packard Laboratories, Palo Alto, California
  • Book: Digital Signal Compression
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511984655.008
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Mathematical transformations
  • William A. Pearlman, Rensselaer Polytechnic Institute, New York, Amir Said, Hewlett-Packard Laboratories, Palo Alto, California
  • Book: Digital Signal Compression
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511984655.008
Available formats
×