most recent 30 from http://mathoverflow.net 2013-05-20T09:00:06Z http://mathoverflow.net/feeds/question/95999 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95999/discrete-wavelet-transform-and-l2-basis warsaga 2012-05-04T16:32:34Z 2012-06-26T08:31:23Z

<p>Using the mother wavlet $phi$ one obtains an orthonormal basis $\phi_{j,k}(x):=2^{j/2}\,\phi(2^j\,x-k)$of L^2 (on the unit interval say). Given a function $f$ on can calculate the coefficients using the $L^2$ inner product. For the Fourier series on can use the discrete fourier transform to do this. How can the discrete wavlet transform be used to calculate the coefficients, here? Does anyone know a good reference?</p> <p>Thanks,</p> <p>warsaga</p>

http://mathoverflow.net/questions/95999/discrete-wavelet-transform-and-l2-basis/96843#96843 warsaga 2012-05-13T16:58:16Z 2012-05-13T16:58:16Z

<p>The best reference I found was www2.isye.gatech.edu/~brani/wp/kidsA.pdf</p> <p>Still not completly satisfactory since the discrete Wavlet transform of the Wavelet psi funciton should just yield one nonzero coefficient.</p>

http://mathoverflow.net/questions/95999/discrete-wavelet-transform-and-l2-basis/100665#100665 Andrei MF 2012-06-26T08:31:23Z 2012-06-26T08:31:23Z

<p>Take a look also at a nice paper "Discrete Wavelet Transformations and Undergraduate Education" at <a href="http://www.ams.org/notices/201105/rtx110500656p.pdf" rel="nofollow">http://www.ams.org/notices/201105/rtx110500656p.pdf</a>.</p>