Orthonormal Polynomial Wavelets on the Interval and Applications to the Analysis of Turbulent Flow Fields
Jochen Fröhlich, Markus Uhlmann · SIAM Journal on Applied Mathematics · 2003
The paper presents an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomials. Expansion coefficients are taken as appropriate roots of the Chebyshev polynomials of the second kind. The new transform is first applied to analytical data, and appropriate definitions of a scalogram are presented. The transform is then extended to the multidimensional case, finding the tensor-product construction more appropriate than the multiresolution. The new method offers the possibility to determine meaningful spectra for signals on bounded domains which are constructed in a global and in a local fashion. Analyses of one- and two-dimensional data from a direct numerical simulation of turbulent channel flow are presented and demonstrate the potential of the method.