Wavelet Transforms

Abstract

Wavelet theory is often seen as an alternative to time-frequency analysis. Like time-frequency analysis, wavelet theory has many roots and has become an interdisciplinary field combining harmonic analysis, applied mathematics, and signal and data processing. An introduction to time-frequency analysis would be incomplete without mention of wavelet theory. This chapter discusses some of the basic ideas in wavelet theory and contrasts them with time-frequency analysis. A few pages certainly cannot do justice to wavelet theory, but there already exist many introductions to wavelet theory, written from various points of view and for audiences on all levels. The books by the founders of wavelet theory, Y. Meyer [202, 204] and I. Daubechies [63], are still unsurpassed, the books by C. Chui [43] and G. Kaiser [175] are recommended as introductions that require fewer mathematical prerequisites, and the state of the art of wavelet theory in signal analysis is represented in S. Mallat’s book [197].