halfplane to be able to reconstruct a signal from the corresponding wavelet coefficients. One such system is the affine system for some real parameters a > 1, b > 0. The corresponding discrete subset of the halfplane consists of all the points (a^m, nb a^m) with m, n in Z. The corresponding child wavelets are now given as

A sufficient condition for the reconstruction of any signal x of finite energy by the formula

is that the functions form an orthonormal basis

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