A tutorial on wavelets from an electrical engineering perspective, part 1:Discrete wavelet techniques

The objective of this paper is to present the subject of wavelets from a fi lter-theory perspective, which is quite familiar to electrical engineers. S uch a presentation provides both physical and mathematical insights into th e problem. II is shown that taking the discrete wavelet transform of a func tion is equivalent to filtering it by a bank of constant-e filters, the non -overlapping bandwidths of which differ by an octave. The discrete wavelets are presented, and a recipe is provided for generating such entities. One of the goals of this tutorial is to illustrate how the wavelet decompositio n is carried out, starting from the fundamentals, and how the scaling funct ions and wavelets are generated from the filter-theory perspective. Example s are presented to illustrate the class of problems for which the discrete wavelet techniques are ideally suited. It is interesting to note that it is not necessary to generate the wavelets or the scaling functions in order t o implement the discrete wavelet transform. Finally, it is shown how wavele t techniques can be used to solve operator/matrix equations. It is shown th at the "orthogonal-transform property" of the discrete wavelet techniques d oes not hold in numerical computations.