Real-valued
•• Beta wavelet
•• Hermitian wavelet
•• Hermitian hat wavelet
•• Meyer wavelet
•• Mexican hat wavelet
•• Shannon wavelet
Complex-valued
[1] Mallat, Stephane. "A wavelet tour of signal processing. 1998." 250-252.
[2] The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. chapter 8 equation 8-1: http://www.dspguide.
com/ch8/4.htm
[3] http://homepages.dias.ie/~ajones/publications/28.pdf
[4] http://www.polyvalens.com/blog/?page_id=15#7.+The+scaling+function+%5B7%5D
[5] http://scienceworld.wolfram.com/biography/Zweig.html Zweig, George Biography on Scienceworld.wolfram.com
[6] P. Hirsch, A. Howie, R. Nicholson, D. W. Pashley and M. J. Whelan (1965/1977) Electron microscopy of thin crystals (Butterworths, London/Krieger, Malabar FLA) ISBN 0-88275-376-2
[7] P. Fraundorf, J. Wang, E. Mandell and M. Rose (2006) Digital darkfield tableaus, Microscopy and Microanalysis 12:S2, 1010–1011 (cf.
arXiv:cond-mat/0403017 (http://arxiv.org/abs/cond-mat/0403017))
[8] M. J. Hÿtch, E. Snoeck and R. Kilaas (1998) Quantitative measurement of displacement and strain fields from HRTEM micrographs, Ultramicroscopy 74:131-146.
[9] Martin Rose (2006) Spacing measurements of lattice fringes in HRTEM image using digital darkfield decomposition (M.S. Thesis in Physics, U. Missouri – St. Louis)
[10] F. G. Meyer and R. R. Coifman (1997) Applied and Computational Harmonic Analysis 4:147.
[11] A. G. Flesia, H. Hel-Or, A. Averbuch, E. J. Candes, R. R. Coifman and D. L. Donoho (2001) Digital implementation of ridgelet packets (Academic Press, New York).
[12] J. Shi, N.-T. Zhang, and X.-P. Liu, "A novel fractional wavelet transform and its applications," Sci. China Inf. Sci., vol. 55, no. 6, pp.
1270–1279, June 2012. URL: http://www.springerlink.com/content/q01np2848m388647/
[13] A.N. Akansu, W.A. Serdijn and I.W. Selesnick, Emerging applications of wavelets: A review (http://web.njit.edu/~akansu/PAPERS/
ANA-IWS-WAS-ELSEVIER PHYSCOM 2010.pdf), Physical Communication, Elsevier, vol. 3, issue 1, pp. 1-18, March 2010.
[14]
[14] An overview of P1901 PHY/MAC proposal.
[15] J. Rafiee et al. Feature extraction of forearm EMG signals for prosthetics, Expert Systems with Applications 38 (2011) 4058–67.
[16] J. Rafiee et al. Female sexual responses using signal processing techniques, The Journal of Sexual Medicine 6 (2009) 3086–96. (pdf) (http:// rafiee.us/files/JSM_2009.pdf)
[17] J. Rafiee and Peter W. Tse, Use of autocorrelation in wavelet coefficients for fault diagnosis, Mechanical Systems and Signal Processing 23 (2009) 1554–72.
[18] Matlab Toolbox – URL: http://matlab.izmiran.ru/help/toolbox/wavelet/ch06_a32.html
References
• Paul S. Addison, The Illustrated Wavelet Transform Handbook, Institute of Physics, 2002, ISBN 0-7503-0692-0
• Ali Akansu and Richard Haddad, Multiresolution Signal Decomposition: Transforms, Subbands, Wavelets, Academic Press, 1992, ISBN 0-12-047140-X
• B. Boashash, editor, "Time-Frequency Signal Analysis and Processing – A Comprehensive Reference", Elsevier Science, Oxford, 2003, ISBN 0-08-044335-4.
• Tony F. Chan and Jackie (Jianhong) Shen, Image Processing and Analysis – Variational, PDE, Wavelet, and Stochastic Methods, Society of Applied Mathematics, ISBN 0-89871-589-X (2005)
• Ingrid Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, 1992, ISBN 0-89871-274-2
• Ramazan Gençay, Faruk Selçuk and Brandon Whitcher, An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, Academic Press, 2001, ISBN 0-12-279670-5
• Haar A., Zur Theorie der orthogonalen Funktionensysteme, Mathematische Annalen, 69, pp 331–371, 1910.
•• Barbara Burke Hubbard, "The World According to Wavelets: The Story of a Mathematical Technique in the Making", AK Peters Ltd, 1998, ISBN 1-56881-072-5, ISBN 978-1-56881-072-0
• Gerald Kaiser, A Friendly Guide to Wavelets, Birkhauser, 1994, ISBN 0-8176-3711-7
• Stéphane Mallat, "A wavelet tour of signal processing" 2nd Edition, Academic Press, 1999, ISBN 0-12-466606-X
• Donald B. Percival and Andrew T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000, ISBN 0-521-68508-7
• Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (2007), "Section 13.10. Wavelet Transforms" (http:// apps.nrbook.com/empanel/index.html#pg=699), Numerical Recipes: The Art of Scientific Computing (3rd ed.), New York: Cambridge University Press, ISBN 978-0-521-88068-8
• P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice Hall, 1993, ISBN 0-13-605718-7
• Mladen Victor Wickerhauser, Adapted Wavelet Analysis From Theory to Software, A K Peters Ltd, 1994, ISBN 1-56881-041-5
•• Martin Vetterli and Jelena Kovačević, "Wavelets and Subband Coding", Prentice Hall, 1995, ISBN 0-13-097080-8
External links
• Hazewinkel, Michiel, ed. (2001), "Wavelet analysis" (http://www.encyclopediaofmath.org/index.php?title=p/
w097160), Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
• OpenSource Wavelet C# Code (http://www.waveletstudio.net/)
• JWave – Open source Java implementation of several orthogonal and non-orthogonal wavelets (https://code.
google.com/p/jwave/)
• Wavelet Analysis in Mathematica (http://reference.wolfram.com/mathematica/guide/Wavelets.html) (A very comprehensive set of wavelet analysis tools)
• 1st NJIT Symposium on Wavelets (April 30, 1990) (First Wavelets Conference in USA) (http://web.njit.edu/
~ali/s1.htm)
• Binomial-QMF Daubechies Wavelets (http://web.njit.edu/~ali/NJITSYMP1990/
AkansuNJIT1STWAVELETSSYMPAPRIL301990.pdf)
• Wavelets (http://www-math.mit.edu/~gs/papers/amsci.pdf) by Gilbert Strang, American Scientist 82 (1994) 250–255. (A very short and excellent introduction)
• Wavelet Digest (http://www.wavelet.org)
• NASA Signal Processor featuring Wavelet methods (http://www.grc.nasa.gov/WWW/OptInstr/
NDE_Wave_Image_ProcessorLab.html) Description of NASA Signal & Image Processing Software and Link to Download
• Course on Wavelets given at UC Santa Barbara, 2004 (http://wavelets.ens.fr/ENSEIGNEMENT/COURS/
UCSB/index.html)
• The Wavelet Tutorial by Polikar (http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html) (Easy to understand when you have some background with fourier transforms!)
• OpenSource Wavelet C++ Code (http://herbert.the-little-red-haired-girl.org/en/software/wavelet/)
• Wavelets for Kids (PDF file) (http://www.isye.gatech.edu/~brani/wp/kidsA.pdf) (Introductory (for very smart kids!))
• Link collection about wavelets (http://www.cosy.sbg.ac.at/~uhl/wav.html)
• Gerald Kaiser's acoustic and electromagnetic wavelets (http://wavelets.com/pages/center.html)
• A really friendly guide to wavelets (http://perso.wanadoo.fr/polyvalens/clemens/wavelets/wavelets.html)
• Wavelet-based image annotation and retrieval (http://www.alipr.com)
• Very basic explanation of Wavelets and how FFT relates to it (http://www.relisoft.com/Science/Physics/
sampling.html)
• A Practical Guide to Wavelet Analysis (http://paos.colorado.edu/research/wavelets/) is very helpful, and the wavelet software in FORTRAN, IDL and MATLAB are freely available online. Note that the biased wavelet power spectrum needs to be rectified (http://ocgweb.marine.usf.edu/~liu/wavelet.html).
• WITS: Where Is The Starlet? (http://www.laurent-duval.eu/siva-wits-where-is-the-starlet.html) A dictionary of tens of wavelets and wavelet-related terms ending in -let, from activelets to x-lets through bandlets, contourlets, curvelets, noiselets, wedgelets.
• Python Wavelet Transforms Package (http://www.pybytes.com/pywavelets/) OpenSource code for computing 1D and 2D Discrete wavelet transform, Stationary wavelet transform and Wavelet packet transform.
• Wavelet Library (http://pages.cs.wisc.edu/~kline/wvlib) GNU/GPL library for n-dimensional discrete wavelet/framelet transforms.
• The Fractional Spline Wavelet Transform (http://bigwww.epfl.ch/publications/blu0001.pdf) describes a fractional wavelet transform based on fractional b-Splines.
• A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity (http://dx.doi.org/10.1016/j.sigpro.2011.04.025) provides a tutorial on two-dimensional oriented wavelets and related geometric multiscale transforms.
• HD-PLC Alliance (http://www.hd-plc.org/)
• Signal Denoising using Wavelets (http://tx.technion.ac.il/~rc/SignalDenoisingUsingWavelets_RamiCohen.
pdf)
• A Concise Introduction to Wavelets (http://www.docstoc.com/docs/160022503/
A-Concise-Introduction-to-Wavelets) by René Puchinger.