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Topic: Wavelet

Related Topics

Wavelet transform

Mexican hat wavelet

Continuous wavelet transform

Haar wavelet

Fourier transform

Fourier integral

Chirplet

Hough transform

Mellin transform

Continuous Fourier transform

Laplace transform

Digital signal processing

Frequency spectrum

Discrete Fourier transform

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	PlanetMath: wavelet
		It is not obvious from the definition that wavelets even exist, or how to construct one; the Haar wavelet is the standard example of a wavelet, and one technique used to construct wavelets.
		Generally, wavelets are constructed from a multiresolution analysis, but they can also be generated using wavelet sets.
		This is version 6 of wavelet, born on 2004-06-24, modified 2004-06-25.
	planetmath.org /encyclopedia/Wavelet.html (219 words)

	Wavelet - ExampleProblems.com
		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).
		All wavelet transforms may be considered to be forms of time-frequency representation and are, therefore, related to the subject of harmonic analysis.
		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.
	www.exampleproblems.com /wiki/index.php/Wavelet (1014 words)

	THE WAVELET TUTORIAL
		Although the discretized continuous wavelet transform enables the computation of the continuous wavelet transform by computers, it is not a true discrete transform.
		Recall that the CWT is a correlation between a wavelet at different scales and the signal with the scale (or the frequency) being used as a measure of similarity.
		One important property of the discrete wavelet transform is the relationship between the impulse responses of the highpass and lowpass filters.
	users.rowan.edu /~polikar/WAVELETS/WTpart4.html (3398 words)

	wavefun (Wavelet Toolbox)
		wavelet obtained after each iteration of the cascade algorithm are shown.
		For compactly supported wavelets defined by filters, in general no closed form analytic formula exists.
		For biorthogonal wavelets, the same ideas can be applied on each of the two multiresolution schemes in duality.
	www.tau.ac.il /cc/pages/docs/matlab/help/toolbox/wavelet/wavefun.html (420 words)

	Wavelets and Signal Processing
		Wavelet transforms (of which there are, at least formally, an infinite number) allow the components of a non-stationary signal to be analyzed.
		This means that the result consists of a wavelet scaling function value (also known as a smooth value or a low pass filter value), followed by bands of wavelet function values (sometimes called wavelet coefficients), in increasing frequency.
		Wavelet compression can be used to estimate the amount of determinism in a particular region of a time series (or, looked at another way, the amount of noise).
	www.bearcave.com /misl/misl_tech/wavelets/index.html (2632 words)

	Wavelet-based Image and Video Compression (Site not responding. Last check: 2007-10-13)
		The wavelet transform is similar to the STFT in that the signal is multiplied by a function similar to windows function in STFT, but the transform is done separately for different segments of the signal.
		For a given mother wavelet, the dimensions of the boxes can be changed, while keeping the area the same, and this is where the power of the wavelets lie.
		Wavelet decomposition can be operated either on the original video samples before the motion compensation or on the residual video samples after motion compensation.
	www.seas.upenn.edu /~ksl/Classes/TCOM502/Wavelets/index.html (2566 words)

	Wavelet Page
		Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale.
		Wavelets are well-suited for approximating data with sharp discontinuities.
		The wavelet analysis procedure is to adopt a wavelet prototype function, called an analyzing wavelet or mother wavelet.
	www.geocities.com /hyungunsong/wavelet.htm (739 words)

	A Linear Algebra View of the Wavelet Transform
		The matrix form of the wavelet transform is both computationally inefficient and impractical in its memory consumption.
		Conceptually the scaling and wavelet functions span larger and larger sections of the signal as the basis decreases.
		The result of the wavelet transform produces a "down sampled" smoothed version of the signal (calculated by the wavelet scaling function) and a "down sampled" version of the signal that reflects change between signal elements.
	www.bearcave.com /misl/misl_tech/wavelets/matrix (1660 words)

	Wavelet Software at Brooklyn Poly
		The wavelet transform provides a multiresolution representation using a set of analyzing functions that are dilations and translations of a few functions (wavelets).
		The dual-tree complex wavelet transform overcomes these limitations - it is nearly shift-invariant and is oriented in 2D [Kin-2002].
		The 2D dual-tree wavelet transform produces six subbands at each scale, each of which are strongly oriented at distinct angles.
	taco.poly.edu /WaveletSoftware (362 words)

	About Wavelet Group - Company Profile
		WAVELET GROUP is an advanced technology company that is fast becoming a trend setter in products and services of the digital signal processing (DSP) and digital image processing technologies.
		WAVELET GROUP was set up in 1995 by Vishwas Udpikar, a Ph.D. in Digital Signal Processing, and the motivation to set it up was to bridge the large gap between the expectations of largely multi-disciplinary applications of DSP and the developers of DSP.
		WAVELET GROUP's philosophy is based on total commitment to clients, partnership, responsiveness and unmatched excellence.
	www.waveletgroup.com /about.htm (319 words)

	Wave:Wavelets 3
		One condition of the wavelet transform is that the average of the wavelet itself must be zero.
		However, it is much simpler to use the fact that the wavelet transform is the convolution between the two functions x and Psi, and to carry out the wavelet transform in Fourier space using the Fast Fourier Transform (FFT).
		The result is that signals in the wavelet transform at one end of the time series will get wrapped around to the other end.
	atoc.colorado.edu /research/wavelets/wavelet3.html (639 words)

	Advanced Concepts (Wavelet Toolbox)
		The Haar wavelet is used to decompose the signal at level 7.
		Wavelet decomposition localizes the period of the sine within the interval [8,16].
		The length of the WP tree leaves is 2; there are 128 leaves, labeled from (7,0) to (7,127) and indexed from 127 to 254.
	www.weizmann.ac.il /matlab/toolbox/wavelet/ch06_50a.html (445 words)

	blitzwave: Wavelet Class Reference
		Integer compatibility means that wavelet decomposition and reconstruction do not use floating point operations on the data.
		Wavelet decomposition and reconstruction may still lead to information loss on integer data if the lifting scheme contains scaling steps.
		Wavelet and scaling coefficients are not automatically normalized after lifting, otherwise integer applications would not be possible.
	blitzwave.sourceforge.net /api/classWavelet.html (553 words)

	Oilfield Glossary: Term 'wavelet'
		The wavelet originates as a packet of energy from the source point, having a specific origin in time, and is returned to the receivers as a series of events distributed in time and energy.
		Wavelets also decay due to the loss of energy as heat during propagation.
		Some wavelets are known by their shape and spectral content, such as the Ricker wavelet.
	www.glossary.oilfield.slb.com /Display.cfm?Term=wavelet (198 words)

	A Really Friendly Guide To Wavelets
		In (1) the wavelet transform is calculated by continuously shifting a continuously scalable function over a signal and calculating the correlation between the two.
		By now we have managed to reduce the highly redundant continuous wavelet transform as formulated in (1) with its infinite number of unspecified wavelets to a finite stage iterated digital filter bank which can be directly implemented on a digital computer.
		The first number is the number of vanishing moments of the analyzing wavelet (the wavelet that decomposes a signal) and the second number is the number of vanishing moments of the synthesizing wavelet (the wavelet that reconstructs the signal).
	perso.orange.fr /polyvalens/clemens/wavelets/wavelets.html (5926 words)

	PyWavelets - Discrete Wavelet Transform in Python
		For biorthogonal wavelet returns scaling and wavelet function both for decomposition and reconstruction.
		A Wavelet object created in this way is a standard Wavelet object and can be used as any other Wavelet object.
		Wavelet transform has recently became very popular when it comes to analysis, denoising and compression of signals and images.
	www.pybytes.com /pywavelets (1728 words)

	Wavelet Explorer: New Generation Signal and Image Analysis
		Wavelet analysis, in contrast to Fourier analysis, uses approximating functions that are localized in both time and frequency space.
		Wavelet Explorer introduces you to this exciting new area and delivers a broad spectrum of wavelet analysis tools to your desktop.
		Wavelet Explorer 1.2.2 requires Mathematica 5.0 or higher and is available for all Mathematica platforms.
	www.wolfram.com /products/applications/wavelet (337 words)

	1996 SIGGRAPH Wavelets in Computer Graphics Course
		With their roots in signal processing and harmonic analysis, wavelets have lead to a number of efficient and easy to implement algorithms.
		Following the success of the wavelets courses at SIGGRAPH 94 and 95 and based on the experiences of the organizers and lecturers, there will be another wavelets course at SIGGRAPH 96.
		Since new wavelet constructions now exist, which are easy to implement and do not require any heavy mathematical machinery to describe, the course will be accessible to those who do not have any prior knowledge of wavelets or a strong background in mathematical Fourier theory.
	www.multires.caltech.edu /teaching/courses/waveletcourse (1976 words)

	Wavelets in Multiresolution Analysis
		In order to move the window about the length of the signal, the wavelets can be translated about time in addition to being compressed and widened.
		There are three important terms to learn for understand vector spaces and these terms of often used in discussions of wavelets with respect to their use in multiresolution analysis.
		As mentioned in the haar wavelet example, there are two kinds of data: the sparse data and the detailed data.
	davis.wpi.edu /~matt/courses/wavelets (1895 words)

	Wavelet Basics (Site not responding. Last check: 2007-10-13)
		The function displayed on the left is a so-called wavelet function from the Daubechies family of wavelet functions.
		Remarkably, the wavelet function (mother wavelet) is orthogonal to all functions which are obtained by shifting the mother right or left by an integer amount.
		The orthonormality of the Daubechies wavelets has a very important mathematical and engineering consequence: any continuous function may be uniquely projected onto the wavelet basis functions and expressed as a linear combination of the basis functions.
	www-star.stanford.edu /projects/sswrg/basics.html (870 words)

	The Haar wavelet transform
		The nice thing is that wavelets are localized since they only live on part of the interval of the data, as opposed to the trigonometric functions used in Fourier analysis which live on the entire interval of the data.
		While it is very important to keep in mind that the wavelet transform can be described by a unitary matrix, it is not efficient to perform the transformation by multiplying the matrix to a vector.
		The way to wavelet transform numerically, is to proceed as in the example in section 5.2.1 by moving the filters
	amath.colorado.edu /courses/4720/2000Spr/Labs/Haar/haar.html (2455 words)

	Wavelet sources
		This is a collection of bibliographies pertaining to wavelets as part of a much larger collection of bibliographies pertaining to various topics in computer science and mathematics.
		The X Wavelet Packet Laboratory is an X based tool to examine 1-D real-valued signals using wavelets and wavelet packets.
		The connection is that wavelets are often used for this sort of work seeing how their multiscale features mesh nicely with the multiscale form of fractals.
	www-ocean.tamu.edu /~baum/wavelets.html (1267 words)

	cwt (Wavelet Toolbox)
		The wavelet coefficient of s at scale a and position b is defined by
		Since s(t) is a discrete signal, we use a piecewise constant interpolation of the s(k) values, k = 1 to
		This example demonstrates the difference between discrete and continuous wavelet transforms.
	www.mathworks.com /access/helpdesk/help/toolbox/wavelet/cwt.html (375 words)

	WAVELETS
		The wavelets all have the same basic form and shape, but the strength or impetus of each wavelet is random and uncorrelated with the strength of the other wavelets...
		The reason is that a new wavelet is born each day to take the place of the one that does die.
		Peter Müller and Brani Vidakovic are editors a volume on Bayesian inference in the wavelet (multiscale) domain.
	www.isye.gatech.edu /~brani/wavelet.html (3093 words)

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