Abstract
Multiresolution theory provides a mathematical framework for constructing orthonormal wavelet bases, and obtaining a fast computation of decomposition coefficients in a wavelet base. The starting point is the approximation of signals x at different scales 2jby linear projections into nested spaces Vj, which define a multiresolution. These projections are calculated by constructing orthonormal bases of each Vj space, expanding and translating a function, called the scale function. These scaling functions are characterized by discrete filters h(n) whose Fourier transforms are specified in order to obtain orthonormal bases of each Vj. Projections into these spaces are computed using an h-filtering algorithm and subsampling at each scale. The Haar wavelet basis corresponds to piecewise constant approximations, calculated by successive averaging.
