Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-18T19:40:14.556Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  23 February 2017

Peter Nickolas
Peter Nickolas
Affiliation:
University of Wollongong, New South Wales
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Wavelets
A Student Guide
 , pp. 259 - 261
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bachman, George, Narici, Lawrence, and Beckenstein, Edward. 2000. Fourier and wavelet analysis. Universitext. Springer-Verlag, New York.
Bartle, Robert G. 1976. The elements of real analysis. Second edn. John Wiley & Sons, New York, London and Sydney.
Berberian, Sterling K. 1994. A first course in real analysis. Undergraduate Texts in Mathematics. Springer-Verlag, New York.
Boggess, Albert, and Narcowich, Francis J. 2009. Afirst course in wavelets with Fourier analysis. Second edn. John Wiley & Sons Inc., Hoboken, NJ.
Carleson, Lennart. 1966. On convergence and growth of partial sums of Fourier series. Acta Math., 116, 135–157.Google Scholar
Chui, Charles K. 1992. An introduction to wavelets. Wavelet Analysis and Its Applications, vol. 1. Academic Press, Inc., Boston, MA.
Daubechies, Ingrid. 1988. Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math., 41(7), 909–996.Google Scholar
Daubechies, Ingrid. 1992. Ten lectures on wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
Daubechies, Ingrid, and Lagarias, Jeffrey C. 1991. Two-scale difference equations. I. Existence and global regularity of solutions. SIAM J. Math. Anal., 22(5), 1388–1410.Google Scholar
Daubechies, Ingrid, and Lagarias, Jeffrey C. 1992. Two-scale difference equations. II. Local regularity, infinite products of matrices and fractals. SIAM J. Math. Anal., 23(4), 1031–1079.Google Scholar
Davis, Philip J. 1975. Interpolation and approximation. Dover Publications, Inc., New York. Re-publication, with minor corrections, of the 1963 original, with a new preface and bibliography.
Debnath, Lokenath, and Mikusiński, Piotr. 1999. Introduction to Hilbert spaces with applications. Second edn. Academic Press, Inc., San Diego, CA.
Goffman, Casper, and Pedrick, George. 1965. First course in functional analysis. Prentice-Hall, Inc., Englewood Cliffs, NJ.
Haar, Alfred. 1910. Zur Theorie der orthogonalen Funktionensysteme. Math. Ann., 69(3), 331–371.Google Scholar
Heil, Christopher. 2011. Abasis theory primer. Expanded edn. Applied and Numerical Harmonic Analysis. Birkhäuser/Springer, New York.
Herńandez, Eugenio, and Weiss, Guido. 1996. A first course on wavelets. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL.
Hong, Don, Gardner, Robert, and Wang, Jianzhong. 2004. Real analysis with an introduction to wavelets and applications. Academic Press, San Diego, CA.
Hubbard, Barbara Burke. 1998. The world according to wavelets. Second edn. A K Peters Ltd, Wellesley, MA.
Kahane, J.-P., and Lemarié-Rieusset, P.-G. 1995. Fourier series and wavelets. Gordon and Breach Science.Google Scholar
Kaiser, Gerald. 1994. A friendly guide to wavelets. Birkhäuser Boston, Inc., Boston, MA.
Katznelson, Yitzhak. 1968. An introduction to harmonic analysis. John Wiley & Sons, Inc., New York, London and Sydney.
Körner, T. W. 2004. A companion to analysis. Graduate Studies in Mathematics, vol. 62. American Mathematical Society, Providence, RI.
Lang, Markus, and Heller, Peter N. 1996. The design of maximally smooth wavelets. Pages 1463–1466 of: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 3. IEEE.
Lang, Serge. 1997. Undergraduate analysis. Second edn. Undergraduate Texts in Mathematics. Springer-Verlag, New York.
Lawton, Wayne M. 1990. Tight frames of compactly supported affine wavelets. J. Math. Phys., 31(8), 1898–1901.Google Scholar
Lawton, Wayne M. 1991. Necessary and sufficient conditions for constructing orthonormal wavelet bases. J. Math. Phys., 32(1), 57–61.Google Scholar
Lemarié-Rieusset, Pierre-Gilles, and Malgouyres, Gérard. 1991 Support des fonctions de base dans une analyse multi-resolution. C. R. Acad. Sci. Paris Sér. I Math., 313(6), 377–380.Google Scholar
Lieb, Elliott H., and Loss, Michael. 2001. Analysis. Second edn. Graduate Studies in Mathematics, vol. 14. American Mathematical Society, Providence, RI.
Lina, Jean-Marc, and Mayrand, Michel. 1993. Parametrizations for Daubechies wavelets. Phys. Rev. E (3), 48(6), R4160–R4163.Google Scholar
Mallat, Stéphane G. 1989. Multiresolution approximations and wavelet orthonormal bases of L2(R). Trans. Amer. Math. Soc., 315(1), 69–87.Google Scholar
Meyer, Yves. 1993. Wavelets. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA. Algorithms and applications. Translated from the French and with a foreword by Ryan, Robert D..
Nievergelt, Yves. 2013. Wavelets made easy. Modern Birkhäuser Classics. Birkhäuser/Springer, New York. Second corrected printing of the 1999 original.
Oppenheim, Alan V., and Schafer, Ronald W. 1989. Discrete-time signal processing. Prentice-Hall, Inc., Englewood Cliffs, NJ.
Percival, Donald B., and Walden, Andrew T. 2000. Wavelet methods for time series analysis. Cambridge Series in Statistical and Probabilistic Mathematics, vol. 4. Cambridge University Press, Cambridge.
Pinsky, Mark A. 2002. Introduction to Fourier analysis and wavelets. Brooks/Cole Series in Advanced Mathematics. Brooks/Cole, Pacific Grove, CA.
Pollen, David. 1989 (May). Parametrization of compactly supported wavelets. Company Report, Aware, Inc., AD890503.1.4.
Pollen, David. 1992. Daubechies’ scaling function on [0, 3]. Pages 3–13 of: Wavelets. Wavelet Anal. Appl., vol. 2. Academic Press, Inc., Boston, MA.
Regensburger, Georg. 2007. Parametrizing compactly supported orthonormal wavelets by discrete moments. Appl. Algebra Engrg. Comm. Comput., 18(6), 583–601.Google Scholar
Royden, H. L., and Fitzpatrick, Patrick. 2010. Real analysis. Fourth, revised edn. Prentice Hall.
Ruch, David K., and Van Fleet, Patrick J. 2009. Wavelet theory. ohn Wiley & Sons, Inc., Hoboken, NJ.
Rudin, Walter. 1976. Principles of mathematical analysis. Third edn. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York, Auckland and D¨usseldorf.
Rudin, Walter. 1987. Real and complex analysis. Third edn. McGraw-Hill Book Co., New York.
Saxe, Karen. 2002. Beginning functional analysis. Undergraduate Texts in Mathematics. Springer-Verlag, New York.
Schneid, J., and Pittner, S. 1993. On the parametrization of the coefficients of dilation equations for compactly supported wavelets. Computing, 51(2), 165–173.Google Scholar
Sen, Rabindranath. 2014. A first course in functional analysis: theory and applications. Anthem Press, London.
Shann, Wei-Chang, and Yen, Chien-Chang. 1997. Exact solutions for Daubechies orthonormal scaling coefficients. Technical Report 9704, Department of Mathematics, National Central University.Google Scholar
Shann, Wei-Chang, and Yen, Chien-Chang. 1999. On the exact values of orthonormal scaling coefficients of lengths 8 and 10. Appl. Comput. Harmon. Anal., 6(1), 109–112.Google Scholar
Simmons, George F. 1963. Introduction to topology and modern analysis. McGraw-Hill Book Co., Inc., New York, San Francisco, CA, Toronto and London.
Spivak, Michael. 1994. Calculus. Third edn. Publish or Perish, Inc., Houston, Texas.
Strichartz, Robert S. 1993. How to make wavelets. Amer. Math. Monthly, 100(6), 539–556.Google Scholar
Stroock, Daniel W. 1999. Aconcise introduction to the theory of integration. Third edn. Birkhäuser Boston, Inc., Boston, MA.
Tolstov, Georgi P. 1962. Fourier series. Translated from the Russian by Silverman, Richard A.. Prentice-Hall, Inc., Englewood Cliffs, NJ.
Walnut, David F. 2002. An introduction to wavelet analysis. Applied and Numerical Harmonic Analysis. Birkhäuser Boston, Inc., Boston, MA.
Wells, Raymond O. Jr., 1993. Parametrizing smooth compactly supported wavelets. Trans. Amer. Math. Soc., 338(2), 919–931.Google Scholar
Wojtaszczyk, P. 1997. A mathematical introduction to wavelets. London Mathematical Society Student Texts, vol. 37. Cambridge University Press, Cambridge.
Young, Nicholas. 1988. An introduction to Hilbert space. Cambridge Mathematical Textbooks. Cambridge University Press, Cambridge.

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Peter Nickolas, University of Wollongong, New South Wales
  • Book: Wavelets
  • Online publication: 23 February 2017
  • Chapter DOI: https://doi.org/10.1017/9781139644280.011
Available formats
×

Save book to Dropbox

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 Dropbox.

  • References
  • Peter Nickolas, University of Wollongong, New South Wales
  • Book: Wavelets
  • Online publication: 23 February 2017
  • Chapter DOI: https://doi.org/10.1017/9781139644280.011
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.

  • References
  • Peter Nickolas, University of Wollongong, New South Wales
  • Book: Wavelets
  • Online publication: 23 February 2017
  • Chapter DOI: https://doi.org/10.1017/9781139644280.011
Available formats
×