Wavelets are a class of a functions used to localize a given function in both space and scaling. A family of wavelets can be constructed from a function wavelet transform has properties which are in some ways superior to a conventional Fourier transform .
An individual wavelet can be defined by
(1)
Then
(2)
and Calderón's formula gives
(3)
A common type of wavelet is defined using Haar functions .
The Season 1 episode "Counterfeit Reality " (2005) of the television crime drama NUMB3RS
See also Fourier Transform ,
Haar Function ,
Lemarié's Wavelet ,
Wavelet Transform Explore with Wolfram|Alpha References Benedetto, J. J. and Frazier, M. (Eds.). Wavelets: Mathematics and Applications. Chui, C. K. An Introduction to Wavelets. Chui, C. K. (Ed.). Wavelets: A Tutorial in Theory and Applications. Chui, C. K.; Montefusco, L.; and Puccio, L. (Eds.). Wavelets: Theory, Algorithms, and Applications. Daubechies, I. Ten Lectures on Wavelets. Erlebacher, G. H.; Hussaini, M. Y.; and Jameson, L. M. (Eds.). Wavelets: Theory and Applications. Foufoula-Georgiou, E. and Kumar, P. (Eds.). Wavelets in Geophysics. Hernández, E. and Weiss, G. A First Course on Wavelets. Hubbard, B. B. The World According to Wavelets: The Story of a Mathematical Technique in the Making, 2nd rev. upd. ed. Jawerth, B. and Sweldens, W. "An Overview of Wavelet Based Multiresolution Analysis." SIAM Rev. 36 , 377-412, 1994. Kaiser, G. A Friendly Guide to Wavelets. Massopust, P. R. Fractal Functions, Fractal Surfaces, and Wavelets. Meyer, Y. Wavelets: Algorithms and Applications. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Wavelet Transforms." §13.10 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Resnikoff, H. L. and Wells, R. O. J. Wavelet Analysis: The Scalable Structure of Information. Schumaker, L. L. and Webb, G. (Eds.). Recent Advances in Wavelet Analysis. Stollnitz, E. J.; DeRose, T. D.; and Salesin, D. H. "Wavelets for Computer Graphics: A Primer, Part 1." IEEE Computer Graphics and Appl. 15 , No. 3, 76-84, 1995. Stollnitz, E. J.; DeRose, T. D.; and Salesin, D. H. "Wavelets for Computer Graphics: A Primer, Part 2." IEEE Computer Graphics and Appl. 15 , No. 4, 75-85, 1995. Strang, G. "Wavelets and Dilation Equations: A Brief Introduction." SIAM Rev. 31 , 614-627, 1989. Strang, G. "Wavelets." Amer. Sci. 82 , 250-255, 1994. Taswell, C. Handbook of Wavelet Transform Algorithms. Teolis, A. Computational Signal Processing with Wavelets. Vidakovic, B. Statistical Modeling by Wavelets. Walker, J. S. A Primer on Wavelets and their Scientific Applications. Walter, G. G. Wavelets and Other Orthogonal Systems with Applications. Weisstein, E. W. "Books about Wavelets." http://www.ericweisstein.com/encyclopedias/books/Wavelets.html . Wickerhauser, M. V. Adapted Wavelet Analysis from Theory to Software. Referenced on Wolfram|Alpha Wavelet Cite this as: Weisstein, Eric W. "Wavelet." From MathWorld https://mathworld.wolfram.com/Wavelet.html
Subject classifications 
, sometimes known as a "mother wavelet," which is confined in a finite interval. "Daughter wavelets" 
are then formed by translation (
) and contraction (
). Wavelets are especially useful for compressing image data, since a wavelet transform has properties which are in some ways superior to a conventional Fourier transform. 
