In mathematics, wavelets, wavelet analysis, and the wavelet transform refers to the representation of a signal in terms of a finite length or fast decaying oscillating waveform (known as the mother wavelet). This waveform is scaled and translated to match the input signal. In formal terms, this representation is a wavelet series, which is the coordinate representation of a square integrable function with respect to a complete, orthonormal set of basis functions for the Hilbert space of square integrable functions. Note that the wavelets in the JPEG2000 standard are biorthogonal wavelets, that is, the coordinates in the wavelet series are computed with a different, dual set of basis functions.

Overview

---

The word wavelet is due to Morlet and Grossman in the early 1980s. They used the French word ondelette - meaning "small wave". A little later it was transformed into English by translating "onde" into "wave" - giving wavelet. Wavelet transforms are broadly classified into the discrete wavelet transform (DWT) and the continuous wavelet transform (CWT). The principal difference between the two is the continuous transform operates over every possible scale and translation whereas the discrete uses a specific subset of all scale and translation values.

Using wavelet theory

---

Wavelet theory is applicable to several other subjects. All wavelet transforms may be considered to be forms of time-frequency representation and are, therefore, related to the subject of harmonic analysis. Almost all practically useful discrete wavelet transforms make use of filterbanks containing finite impulse response filters. The wavelets forming a CWT are subject to Heisenberg's uncertainty principle and, equivalently, discrete wavelet bases may be considered in the context of other forms of the uncertainty principle.

More on [ Wavelet ]

Wiley: All New Mathematics & Statistics Titles

Loss Models: From Data to Decisions, Solutions Manual, 3rd Edition
Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot Mon, 25 Aug 2008 04:00:00 -0000
  Loss Models: From Data to Decisions, Third Edition has been thoroughly revised and updated to include new material related to Exam C (old Exam 4) of the Society of Actuaries' accreditation program. Terms are defined when they are first introduced, and a solid background in mathematical sciences (including calculus) is recommended. Companion software, datasets, and over 400 sample test exercises, Read More...
Solved Problems in Geostatistics
Oy Leuangthong, K. Daniel Khan, Clayton V. Deutsch Mon, 25 Aug 2008 04:00:00 -0000
  Solved Problems in Geostatistics brings together exercises and projects that demonstrate key principles and build strong bridges between theory and practice. Each chapter focuses on a comprehensive topic with examples and problems for a technologically evolving audience. Problems in each chapter are classified as analytical, numerical, or practical; exercises are identified as foundational, advanced, Read More...
Practical Text Mining with Perl
Roger Bilisoly Mon, 18 Aug 2008 04:00:00 -0000
  Provides readers with the methods, algorithms, and means to perform text mining tasks This book is devoted to the fundamentals of text mining using Perl, an open-source programming tool that is freely available via the Internet (www.perl.org). It covers mining ideas from several perspectives--statistics, data mining, linguistics, and information retrieval--and provides readers with the means to successfully complete text mining tasks on their Read More...
Loss Models: From Data to Decisions, 3rd Edition Set
Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot Fri, 15 Aug 2008 04:00:00 -0000
This set contains: 9780470187814 Loss Models: From Data to Decisions, 3rd Edition and the 9780470385715 3rd Edition Solutions Manual by Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot. Read More...
An Introduction to Linear Programming and Game Theory, 3rd Edition
Paul R. Thie, Gerard E. Keough Mon, 11 Aug 2008 04:00:00 -0000
  Introduction to Linear Programming and Game Theory, Third Edition includes various additions as well as improvements that have been developed over the last decade, and the most significant addition to the text involves technology. It features an introduction, discussion, and utilization of Solver, a spreadsheet software package that solves mathematical programming problems. PRT Simplex, a computer application for learning the simplex method, Read More...
The Probabilistic Method, 3rd Edition
Noga Alon, Joel H. Spencer Mon, 11 Aug 2008 04:00:00 -0000
  This Third Edition of The Probabilistic Method reflects the most recent developments in the field while maintaining the standard of excellence that established this book as the leading reference on probabilistic methods in combinatorics. Maintaining its clear writing style, illustrative examples, and practical exercises, this new edition emphasizes methodology, enabling readers to use probabilistic techniques for solving problems in such fields Read More...

Subscribe to Math RSS feed