Skip to main content Accessibility help
×
×
Home
Wavelets

Book description

This text offers an excellent introduction to the mathematical theory of wavelets for senior undergraduate students. Despite the fact that this theory is intrinsically advanced, the author's elementary approach makes it accessible at the undergraduate level. Beginning with thorough accounts of inner product spaces and Hilbert spaces, the book then shifts its focus to wavelets specifically, starting with the Haar wavelet, broadening to wavelets in general, and culminating in the construction of the Daubechies wavelets. All of this is done using only elementary methods, bypassing the use of the Fourier integral transform. Arguments using the Fourier transform are introduced in the final chapter, and this less elementary approach is used to outline a second and quite different construction of the Daubechies wavelets. The main text of the book is supplemented by more than 200 exercises ranging in difficulty and complexity.

Reviews

'Not only does it bring the subject in a most suitable and systematic way that, I am sure, mathematics students are used to and probably appreciate most. It is also following some good rules of didactics taking the students by the hand and bringing them to a higher level of understanding, ensuring that at least the bulk of the students does not declutch. A lot of effort is put into taking the rungs of the ladder at just the right pace, not boringly slow or not frighteningly fast, and always placing a chapter in the proper context: what has been achieved, and where do we want to go?'

Adhemar Bultheel Source: European Mathematical Society

'What is really nice with this book is its style, which leads the student step by step through different ideas, theorems and proofs. It explains the reason behind new concepts, discusses their shortcomings, and uses these as a motivation to introduce other concepts.'

Salim Salem Source: MAA Reviews

Refine List
Actions for selected content:
Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive
  • Send content to

    To send 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 sending content to .

    To send content items to your Kindle, first ensure no-reply@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 sending to your Kindle.

    Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent 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.

    Please be advised that item(s) you selected are not available.
    You are about to send
    ×

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×
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.
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.
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.
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.
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.
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.
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.
Lawton, Wayne M. 1991. Necessary and sufficient conditions for constructing orthonormal wavelet bases. J. Math. Phys., 32(1), 57–61.
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.
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.
Mallat, Stéphane G. 1989. Multiresolution approximations and wavelet orthonormal bases of L2(R). Trans. Amer. Math. Soc., 315(1), 69–87.
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.
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.
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.
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.
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.
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.
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.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed