Mani Mehra
Abstract
A collection of the Matlab routines that compute the values of the scaling and wavelet functions (φ(x) and ψ(x) respectively) and the derivative of an arbitrary function (periodic or non periodic) using wavelet bases is presented. Initially, the case of Daubechies wavelets is taken and the procedure is explained for both collocation and Galerkin approaches. For each case a Matlab routine is provided to compute the differentiation matrix and the derivative of the function f(d) = D(d)f. Moreover, the convergence of the derivative is shown graphically as a function of different parameters (the wavelet genus, D and the scale, J) for two test functions. We then consider the use of spline wavelets.
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Index Terms
- Algorithm 929: A suite on wavelet differentiation algorithms
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