wavelet

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wavelet

[′wāv·lət]
(mathematics)
One of a collection of mathematical functions that serve as the elementary building blocks of a mathematical tool for analyzing and synthesizing functions, and for forming representations of signals in both time and frequency.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

wavelet

A small shock wave, usually present in large numbers in boundary layers and around the surface of a supersonic body. Also called a Mach wave or a Mach wavelet
An Illustrated Dictionary of Aviation Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved

wavelet

(mathematics)
A waveform that is bounded in both frequency and duration. Wavelet tranforms provide an alternative to more traditional Fourier transforms used for analysing waveforms, e.g. sound.

The Fourier transform converts a signal into a continuous series of sine waves, each of which is of constant frequency and amplitude and of infinite duration. In contrast, most real-world signals (such as music or images) have a finite duration and abrupt changes in frequency.

Wavelet transforms convert a signal into a series of wavelets. In theory, signals processed by the wavelet transform can be stored more efficiently than ones processed by Fourier transform. Wavelets can also be constructed with rough edges, to better approximate real-world signals.

For example, the United States Federal Bureau of Investigation found that Fourier transforms proved inefficient for approximating the whorls of fingerprints but a wavelet transform resulted in crisper reconstructed images.

SBG Austria.

["Ten Lectures on Wavelets", Ingrid Daubechies].
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)

Google Wave

Web-based collaborative software from Google that offered group instant messaging along with document editing and history. Introduced in beta in 2009, Google shuttered the service in 2010 due to limited acceptance. Components migrated to other Google endeavors.

Each "wave" was a live conference thread viewed by all participants who could edit the content and also add other individuals. In addition, a wave could be played back from the beginning to review the conversation.

Waves, Wavelets and Embedded Waves
A wave was the entire message thread, and a "wavelet" was a subset of the wave that could be created and managed separately. An "embedded wave" was a wave that was placed on a website to provide a chat room or contact method.

Blips and Documents
A "blip" was one message in a wave, and a "document" was the content within a blip.

Gadgets and Robots
"Gadgets" and "robots" added functionality. A gadget was a mini-application, and a robot automatically triggered events. See Google+ and Google.

wavelet compression

A lossy compression method used for color images and video. Instead of compressing small blocks of 8x8 pixels (64 bits) as in JPEG and MPEG, the wavelet algorithms compress the entire image with ratios of up to 300:1 for color and 50:1 for gray scale.

Wavelet compression also supports nonuniform compression, where specified parts of the image can be compressed more than others. There are several proprietary methods based on wavelet mathematics, which are available in products from companies such as Summus, Ltd. (www.summus.com) and Algo Vision LuraTech GmbH (www.luratech.com). See lossy compression and JPEG 2000.


Amazing Compression Ratios
This picture was compressed at 156:1 with InfinOp's Lightning Strike software. The original file was more than a million bytes and compressed down to 7.5K. This image is amazingly good especially considering that it contains only 128 colors. (Image courtesy of InfinOp, Inc.).
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References in periodicals archive ?
Iyengar, "Wavelet Analysis in Current Cancer Genome Research: A Survey", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.
In this paper, we use wavelet analysis to address the issue of EEG feature extraction in P300 Speller BCI.
Timoteo et al., "Alterations in autonomic response during head-up tilt testing in paroxysmal atrial fibrillation patients: a wavelet analysis," Revista Portuguesa de Cardiologia, vol.
The validated results show that the moving [V.sub.n](t, s)-statistic based on wavelet-based multiresolution analysis effectively identifies the breakpoint of the memory of the specific multifractal level after decomposing it through wavelet analysis. The moving [V.sub.n](t, s)-statistic method can eliminate multivariate memory from the different window selected.
Periods Based on Morlet Wavelet Analysis. The periodic fluctuation of precipitation results in the up and down of runoff, so it is important to correctly understand the periodic variation of precipitation.
The result of the wavelet analysis of 3D images, however, depends on the colour/texture of the surface of the object.
Wickerhauser, Adapted wavelet analysis: from theory to software, AK Peters/CRC Press, 1994.
The signal processing techniques employed which is the Fast Fourier Transform (FFT) and Wavelet Analysis (WA) provided in the MATLAB Software.
For brain wave data, first apply binary conversion algorithm and waveform reconstruction algorithm in wavelet analysis to process specific brain wave vector data, select specific wavelet generating function, construct an n scale, from 2[sup]0 to 2[sup]n to conduct binary conversion algorithm:
and Foufoula-Georgiou, E.: 1997, Wavelet analysis for geophysical applications.
Coming fill the limits of the spectral analysis, wavelet analysis has been proposed as a time-frequency advanced method.
Therefore, compare to the Curvelet analysis detection results, the detectability of bigger block size of Wavelet analysis is lower.

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