Introduction

Wavelets were discovered in the eighteenth century, essentially in pertroleum extraction. Compared to the Fourier theory, wavelets are mathematical functions permitting themselves to cut up data into different components relative to the frequency spectrum and next focus on these components somehow independently, extracting their characteristics and lifting to the original data. This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book presents the notion of wavelets as analyzing functions and as mathematical tools for analyzing square integrable functions known in signal theory as finite variance and/or finite energy signals. It offers a general context of Euclidean wavelet analysis by a higher-dimensional analogue.