Wavelets theory and its applications are rapidly developing fields in applied mathematics and signal analysis. Wavelet basis representation of certain signals show advantages over the traditional Fourier basis representation both theoretically and practically. Illustration of the sequence of multiresolution analysis subspaces . is the orthogonal complement of in .
Space represents the space that contains the finest resolution data, and .
The MRA of is a set of nested, closed subspaces , such that where the basis for the subspace is a set of orthonormal, translated functions, and each of these functions sets is a fixed dilation of the scaling function, . In this paper, the data projected onto the subspace is referred as the decomposition of data at resolution level . We define the projection of a function on to be . Decomposition of a Ricker wavelet at increasingly coarser resolution levels. The bases of the decompositions are Daubechies wavelets with and vanishing moments for the left and right figure respectively.