Wavelet decomposition for non-uniform 2D data sequences

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I have a list which is almost surely some sort of a wave-like oscillation:

y(x): {{x_1, y_1}, ...,{x_n, y_n}}

and want to find wavelets that interpolate this data best using Mathematica. However, Mathematica's wavelet toolbox accepts standard sequential (uniform) series rather than non-uniform grids.

Possible solutions are either to firstly interpolate y to a uniform x grid and then proceed with wavelet decomposition or to find a fit to wavelet functions explicitly using FindFit routines without referring to the toolbox.

Is there any other solutions?

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