• SIMULATION RESULTS FOR WAVELET APPROXIMATION

Abstract

We investigate expansions of three functions with respect to 5 wavelet bases. Direct and inverse theorems for wavelet approximation in C and L norms are proved. For the functions possessing local regularity we study the rate of point wise convergence of wavelet Fourier series. We also define and investigate the “Discrete Wavelet Fourier transform” (DWFT) for periodic wavelets generated by a compactly supported scaling function. The DWFT has one important advantage for numerical problems compared with the corresponding wavelet Fourier coefficients: while fast computational algorithms for wavelet Fourier coefficients are recursive, DWFTs can be computed by explicit formulas without any recursion and the computation is fast enough.

The wavelet experiments in the function approximation uses five wavelets like Haar (Haar) wavelet, Debauches (db) wavelet, Symlets (sym) wavelet, Coiflet (coif) wavelet and Biorthogonal (bio) wavelet for the three functions Continuous Exponential Function (case-1), Continuous Periodic Function (Case -2) and Piecewise continuous function (Case -3).All the approximations are carried out for the data length of 2000 data points up to the level 5. The details and approximation are given below.