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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.


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


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].

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.).
References in periodicals archive ?
Embedded Zero Tree Wavelet (EZW): The algorithm EZW is based on lossless image compression technique, and enables a scalable image transmission.
Pixels belong to noise and edge in the image are located at high-frequency components of wavelet: horizontal, vertical, and diagonal coefficients.
For this purpose, the flicker characteristics of the electric arc furnace (EAF) and ladle furnace (LF) are investigated in this paper by using statistical methods, spectral analysis, and multi-resolution wavelet analysis.
This paper discusses a concept of multiframe model and adopts multiple TOFD images, in the sense of the combination of wavelet transform and image registration, SNR and the quality of the image can be enhanced by blending the denoised images together.
A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most relevant to discrete wavelet transforms (DWT) and the justification for the algorithm of the fast wavelet transform (FWT).
In this paper, we construct a quadratic spline wavelet basis on the interval and on the unit square that is well-conditioned and adapted to homogeneous Dirichlet boundary conditions of the first order.
Subsequently a two-dimensional wavelet transform is applied and correlated features are extracted using symmetric uncertainty ranking based filter.
Unlike the wavelet transform, the empirical mode decomposition (EMD) can be decomposed adaptively according to the trend of the signals.
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero.
What is important is that it is unnecessary to calculate the CV for the wavelet transform, and therefore not a one operation with the wavelets needs the CV.

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