WAVELETS: AN ELEMENTARY INTRODUCTION AND EXAMPLES

Wavelets have been found to be very useful in many scientific and engineering applications including computer graphics, scientific visualization, data compression and signal processing. Unfortunately, the two most well known monographs on wavelets by Chui and Daubechies are still unaccessible to a beginner due to the level of mathematical sophistication needed to go through these monographs. Moreover both these monographs introduce wavelets from a signal processing perspective. The objective here is to introduce wavelets via scaling functions using the theory of multiresolution analysis. The primary focus is to describe many examples of scaling functions and their corresponding wavelets without proofs. The two-scale reconstruction and decomposition relations are described in order to provide the reader with a quick working knowledge of wavelets. Examples of wavelets included in this monograph are Haar wavelets, B-spline wavelets and Daubechies wavelets on real line, and Legendre wavelets and flatlet wavelets on bounded intervals.