The last decade has seen an explosion of interest in wavelets, a subject area that has coalesced from roots in mathematics, physics, electrical engineering and other disciplines. As a result, wavelet methodology has had a significant impact in areas as diverse as differential equations, image processing and statistics. This book is an introduction to wavelets and their application in the analysis of discrete time series typical of those acquired in the physical sciences. While we present a thorough introduction to the basic theory behind the discrete wavelet transform (DWT), our goal is to bridge the gap between theory and practice by

1. • emphasizing what the DWT actually means in practical terms;

2. • showing how the DWT can be used to create informative descriptive statistics for time series analysts;

3. • discussing how stochastic models can be used to assess the statistical properties of quantities computed from the DWT; and

4. • presenting substantive examples of wavelet analysis of time series representative of those encountered in the physical sciences.

To date, most books on wavelets describe them in terms of continuous functions and often introduce the reader to a plethora of different types of wavelets. We concentrate on developing wavelet methods in discrete time via standard filtering and matrix transformation ideas.