Orthonormal Polynomial Wavelets on the Interval and Applications to the Analysis of Turbulent Flow Fields

J. Fröhlich, M. Uhlmann
2003 SIAM Journal on Applied Mathematics  
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 of
more » ... bulent channel flow demonstrate the potential of the method.
doi:10.1137/s0036139902404116 fatcat:klrphnzypvfthd5bk737xdctyq