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We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomials. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind. The one-dimensional transform is applied to analytical data and appropriate definitions of a scalogram as well as local and global spectra are presented. The transform is then extended to the multi-dimensional case. Analyses of one-and twodimensional data from a direct numerical simulation ofdoi:10.1137/s0036139902404116 fatcat:klrphnzypvfthd5bk737xdctyq