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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?



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For practitioners I recommend Mallat's "Wavelet Tour of Signal Processing". – Dirk May 4 '12 at 18:26
In the way you stated the question it is to vague: I think if you would make it more precise, then it will attract more attention. – Kirill Shmakov May 4 '12 at 19:14

The best reference I found was

Still not completly satisfactory since the discrete Wavlet transform of the Wavelet psi funciton should just yield one nonzero coefficient.

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Take a look also at a nice paper "Discrete Wavelet Transformations and Undergraduate Education" at

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