A transform which localizes a function both in space and scaling and has some desirable properties compared to the Fourier transform. The transform is based on a wavelet matrix, which can be computed more quickly than the analogous Fourier matrix.
Wavelet Transform
See also
Daubechies Wavelet Filter, Lemarie's Wavelet, Wavelet MatrixExplore with Wolfram|Alpha
References
Daubechies, I. Ten Lectures on Wavelets. Philadelphia, PA: SIAM, 1992.DeVore, R.; Jawerth, B.; and Lucier, B. "Images Compression through Wavelet Transform Coding." IEEE Trans. Information Th. 38, 719-746, 1992.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. Cambridge, England: Cambridge University Press, pp. 584-599, 1992.Strang, G. "Wavelet Transforms Versus Fourier Transforms." Bull. Amer. Math. Soc. 28, 288-305, 1993.Referenced on Wolfram|Alpha
Wavelet TransformCite this as:
Weisstein, Eric W. "Wavelet Transform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WaveletTransform.html