ABSTRACT
To some extent wavelets are no more different than other orthogonal systems. They are an extension of Fourier analysis and used to represent a function by a series of orthogonal functions, but with these differences: The wavelet series converge pointwise, are more localized, exhibit edge effects better, and use fewer coefficients to represent certain signals and images. However, wavelet expansions undergo excessive changes under arbitrary translations, which makes the situation much worse than the Fourier series. We study wavelets in the same manner as in the previous chapters with other orthogonal systems, in particular with orthogonal polynomials and Fourier series. Wavelets are computed by fast transforms.
