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	Wavelet - Wikipedia, the free encyclopedia
		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).
		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.
	en.wikipedia.org /wiki/Wavelet (1236 words)

	Encyclopedia: Haar wavelet (Site not responding. Last check: 2007-10-22)
		Daubechies 20 2-d wavelet (Wavelet Fn X Scaling Fn) Named after Ingrid Daubechies, the orthogonal Daubechies wavelets are a class of wavelets characterized by a maximal number of vanishing moments for some given support.
		The Haar wavelet is the first known wavelet 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).
		The disadvantage of the Haar wavelet is that it is not continuous In mathematics, a continuous function is a function in which arbitrarily small changes in the input produce arbitrarily small changes in the output.
	www.nationmaster.com /encyclopedia/Haar-wavelet (609 words)

	Discussion (Site not responding. Last check: 2007-10-22)
		Wavelet transforms are used extensively in the field of image processing to decompose sets of discrete image data.
		The Haar basis and related wavelet packet bases[13] can not be used for standard wavelet encoding because the profiles of the basis functions are impractical to excite.
		Using this digital wavelet approach, the power of wavelet processing is being further exploited in our laboratory to develop new dynamically adaptive imaging strategies for both functional[18] and interventional MRI applications.
	www.spl.harvard.edu:8000 /pages/papers/panych/new_wave-enc/node11.html (1034 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)

	The Wavelet Digest :: View topic - A naive question about Haar Wavelet!!!!!
		Haar wavelet it's not an exception to other wavelets regarding to the cut-off frequency.
		The sampling theorem tells that the frequency band of your signal is the half of the sampling frequency, and the wavelet decomposition is known to split the frequency band into two frequency bands with equal width, thus the cut off frequency is the quarter of the sampling frequency.
		Wavelet is powerful for transient signal analysis, such as sigularity/breakdown point detection, severe frequency modulation.
	www.wavelet.org /phpBB2/viewtopic.php?p=3759 (409 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.
		The way to wavelet transform numerically, is to proceed as in the example in section 5.2.1 by moving the filters
		A vector which is the Haar transformation of the vector you gave as input corresponding to the level you gave as an input.
	amath.colorado.edu /courses/4720/2000Spr/Labs/Haar/haar.html (2455 words)

	WaveletWadingPool.html
		By directly applying the wavelet transform, the paper hopes to show the reader how some simple wavelets work, by way of introduction to the heavier mathematics that are justified by these initial attempts.
		The wavelet can be expressed as a linear combination of the basis vectors for the higher detail space, since it lies inside the higher resolution space which is spanned by those basis functions.
		This seems justifiable since two wavelet vectors that are not orthogonal that are both quantized introduce more error in the direction that they are not orthogonal, possibly exceeding the threshold for error that we are trying to control during the quantization step.
	www.cgl.uwaterloo.ca /~anicolao/wadingpool/WaveletWadingPool.html (2076 words)

	Piecewise-Linear Haar (Site not responding. Last check: 2007-10-22)
		The range of the non-normalized Haar transform, as measured along the axes, is larger than that of the domain (twice the domain, actually).
		Haar transform but without the normalization by SQRT(2)), we see that there is a lot of empty space between points in the range.
		The Haar is a 45-degree (or one-eighth) rotation of the domain about the origin.
	graphics.cs.ucdavis.edu /~jgseneca/Projects/PLHaar/PLHaar.html (1071 words)

	GNU Scientific Library -- Reference Manual - Wavelet Transforms (Site not responding. Last check: 2007-10-22)
		The is the Daubechies wavelet family of maximum phase with k/2 vanishing moments.
		Thus the resulting visualization of the coefficients of the wavelet transform in the phase plane is easier to understand.
		The "standard" transform performs a complete discrete wavelet transform on the rows of the matrix, followed by a separate complete discrete wavelet transform on the columns of the resulting row-transformed matrix.
	www.gnu.org /software/gsl/manual/gsl-ref_30.html (1074 words)

	Wavelet Based Steganography and Watermarking
		There is a push toward the use of wavelets in signal processing and analysis in place of (or in addition to) the Discrete Cosine Transform (DCT), which is used in the JPEG standard for image compression.
		The Haar transform is one of the simplest transforms in wavelet mathematics.
		The 2D Haar Transform also works on a set of 4 pixels, but is considered "2D" because there is additional processing on a 2 x 2 block after the initial row and column transformations are completed.
	www.cs.cornell.edu /topiwala/wavelets/report.html (3798 words)

	Mehr zu "Haar-Wavelet" bei Metando (Site not responding. Last check: 2007-10-22)
		The disadvantage of the Haar wavelet is that it is not continuous and..
		The Haar wavelet is also the simplest possible wavelet.....2×2 Haar matrix that is associated with the Haar wavelet is..
		The Haar wavelet is the first known wavelet and was.....2×2 Haar matrix that is associated..the Haar wavelet is..
	www.metando.de /search_Haar-Wavelet_0.html (481 words)

	Wavelets in Multiresolution Analysis
		Given four points of data, say values of a pixel in an image, the haar wavelet can be used to compress this data through a process called averaging and differencing.
		As mentioned in the haar wavelet example, there are two kinds of data: the sparse data and the detailed data.
		These coefficients are extracted from the original set of number by using two kinds of filters, high pass (details) and low pass (average.) The two filters are applied, the filtered data from the high pass filter is stored as coefficients for later reconstruction of the signal.
	davis.wpi.edu /~matt/courses/wavelets (1895 words)

	Applying the Haar Wavelet Transform to Time Series Information
		In the wavelet literature this tree structured recursive algorithm is referred to as a pyramidal algorithm.
		Wavelet algorithms are recursive and the smoothed data becomes the input for the next step of the wavelet transform.
		The Haar wavelet algorithms published here are applied to time series where the number of samples is a power of two (e.g., 2, 4, 8, 16, 32, 64...) The Haar wavelet uses a rectangular window to sample the time series.
	www.bearcave.com /misl/misl_tech/wavelets/haar.html (6156 words)

	The Wavelet Approach
		In analogy to the Fourier transform (whose coefficients represent the function over its entire support), the wavelet transform takes the inner product of a function f(t) with a doubly indexed family of functions psi(a,b)=a^{-1/2}psi[(t-b)/a] (the ``wavelets functions'') which are obtained by dilations (by a) and translations (by b) of the ``mother wavelet'' psi.
		Among the many choice of wavelet bases, we have used one of the simplest and actually the oldest example of a discrete wavelet basis to process MACRO waveforms: the so-called Haar [10] basis.
		A key issue is obtaining the wavelet transform of a candidate waveform is defining its size, i.e., the number of samples that will be fed into the algorithm at a time.
	www.cithep.caltech.edu /~kats/rep/node6.html (794 words)

	Anti-aliasing - Wikipedia, the free encyclopedia
		Some basic waves yield anti-aliasing algorithms which are not so good (for instance, the Haar wavelet gives the uniform averaging algorithm.) However, some wavelets are good, and it is possible that some wavelets are better at approximating the functioning of the human brain than the cosine basis.
		Functions based on the Gaussian function are natural choices, because convolution with a Gaussian gives the same result, whether applied to x and y or to the radius.
		Another of its properties is that it (similarly to wavelets) is half way between being localized in the configuration (x and y) and in the spectral (j and k) representation.
	en.wikipedia.org /wiki/Anti-aliasing (2604 words)

	Kolaczyk: Wavelets.
		The Haar wavelet itself is just the difference of two scale functions at one scale finer (up to a normalizing constant).
		This wavelet and scale function are also due to Ingrid Daubechies, but in this particular case additional conditions have been incorporated so as to achieve a nearly symmetric shape in the wavelet.
		A key reason for the incredible success with which wavelets have integrated themselves into the scientific landscape is the fact that a fast, discrete implementation of the mathematics exists.
	math.bu.edu /people/kolaczyk/wavelets.html (860 words)

	Haar (Site not responding. Last check: 2007-10-22)
		Wavelets are mathematical functions that were developed by scientists working in several different fields for the purpose of sorting data by frequency.
		Unlike the discrete cosine transform, the wavelet transform is not Fourier-based and therefore wavelets do a better job of handling discontinuities in data.
		The Haar wavelet operates on data by calculating the sums and differences of adjacent elements.
	www.owlnet.rice.edu /~elec301/Projects99/imcomp/Haar.htm (194 words)

	Haar Wavelet Basis (Site not responding. Last check: 2007-10-22)
		Wavelets, discovered in the last 15 years, are another kind of basis for L
		In Haar wavelet basis, the basis functions are scaled and translated versions of a "mother wavelet" ψ(t).
		This demonstration lets you create a signal by combining Haar basis functions, illustrating the synthesis equation of the Haar Wavelet Transform.
	cnx.rice.edu /content/m10764/latest (246 words)

	Example Wavelets (Site not responding. Last check: 2007-10-22)
		The Haar wavelet is the most fundamental of the wavelet systems and is also known as the length-2 Daubechies filter (See figure 1).
		It is important to note that the Haar wavelet system is the only one that is orthogonal, symmetric, and has compact support.
		The Sinc wavelet is the second fundamental of the wavelet systems (see figure 2).
	cnx.rice.edu /content/m11150/latest (358 words)

	2004-42: Nonuniform Sparse Approximation with Haar Wavelet Basis (Site not responding. Last check: 2007-10-22)
		Sparse approximation theory concerns representing a given signal on $N$ pointsas a linear combination of at most $B$ ($B\ll N$) elements from a dictionary so that the error of the representation is minimized; traditionally, error is taken {\em uniformly} as the sum of squares of errors at each point.
		Parseval's theorem from 1799 which is central in solving uniform sparse approximation for Haar wavelets does not help under nonuniform importance.
		We present the first known polynomial time for the problem of finding $B$ wavelet vectors to represent a signal of length $N$ so that the representation has the smallest error, averaged over the given importance of the points.
	dimacs.rutgers.edu /TechnicalReports/abstracts/2004/2004-42.html (203 words)

	Trading System Solutions - Software - eSignal Solutions - Wavelet Transform Dll - Overview - Redundant Haar wavelet (Site not responding. Last check: 2007-10-22)
		We use Redundant Haar wavelet transformation that represents an initial price series by the sum of the band pass filters named wavelets, and the residual low-frequency filter:
		It is possible to read about Redundant Haar wavelets at http://www.multiresolution.comin more details.
		If the signal is identified then the appropriate wavelet remains without change.
	www.tsresearch.com /software/esignal/eswavelet/overview/haar (252 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Properties of wavelet, continuous/discrete wavelet transform, multiresolution formulation, scaling function and wavelet function that works as filter, subsampling, energy conservation, inverse wavelet transform for reconstruction, 2D wavelet transform, drawbacks of Haar wavelet are also investigated.
		Using wavelets, we represent the signal in the time-scale domain instead of the time-frequency domain because the term “frequency” is reserved for the Fourier transform not just because the frequency and scale works opposite indeed.
		It is concluded that the wavelet is an absolutely excellent tool for image compression but the choice of appropriate wavelet according to the application remains as a future task.
	pages.cpsc.ucalgary.ca /~ylee/projectreport_wavelet.doc (2006 words)

	Using wavelets for data generation
		Wavelets are proposed as a non-parametric data generation tool.
		The idea behind the suggested method is decomposition of data into its details and later reconstruction by summation of the details randomly to generate new data.
		A Haar wavelet is used because of its simplicity.
	ideas.repec.org /a/taf/japsta/v28y2001i2p157-166.html (225 words)

	Haar Wavelet Transform
		To calculate the Haar transform of an array of n samples:
		For better image quality, the quantization algorithm could be tuned to value coefficients based on their position (upper-left is more significant/obvious than lower right), and to degrade them gradually (using division or bit shifting) rather than zeroing them out.
		haar.c - forward and reverse Haar transforms, and a simple quantizer to simulate artifacts with.
	dmr.ath.cx /gfx/haar (284 words)

	Some Recent Papers of F. Murtagh
		Beverly, J. Mason, "A wavelet, Fourier and PCA data analysis pipeline: application to distinguishing mixtures of liquids", Journal of Chemical Information and Computer Sciences, 43, 587-594, 2003.
		F. Murtagh, The Haar wavelet transform of a dendrogram - I.
		JL Starck, MK Nguyen and F Murtagh, Wavelets and curvelets for image deconvolution: a combined approach.
	www.cs.rhul.ac.uk /home/fionn/papers (1197 words)

	Haar Wavelet Coefficient Value Calculation with Sorting (Professional Only) (Site not responding. Last check: 2007-10-22)
		Calculates discrete Haar wavelet transform of X over the last n points.
		The value of Smoothing (bias) coefficient is not included in the sorting (as it has different nature) and it can be accessed through WaveletValueHaar (X,n,1).
		This indicator provides the possibility to estimate relative significance of several largest wavelets.
	www.neuroshell.com /indicators/NSTRDINDHaar_Wavelet_Coefficient00000770.html (101 words)

	Walsh Functions
		The discrete Haar wavelet basis is obtained by choosing the second block in each row and the first and second entry on the last row.
		It is easy to see that any collection of blocks in the rectangle with the property that their shadow intervals form a disjoint cover of the full range provides a collection of patterns forming a basis.
		Since all transformations were orthogonal we must have that the collection of vectors corresponding to this choice of patterns is an orthogonal basis of
	www.math.yale.edu /pub/wavelets/software/xwpl/html/manual/node31.html (420 words)

	WV_FN_HAAR
		The WV_FN_HAAR function constructs wavelet coefficients for the Haar wavelet function.
		The Haar wavelet is the same as the Daubechies wavelet of order 1.
		The IDL Wavelet Toolkit must be licensed on your system to be able to use this function.
	www.astro.princeton.edu /~esirko/idl_html_help/ref12.html (133 words)

	The Wavelet Digest :: View topic - Question: Optimizations for image compression using Haar wavelet
		The Wavelet Digest :: View topic - Question: Optimizations for image compression using Haar wavelet
		Take the integer-2integer version of Haar transform of the image (also known as the S
		Second stage: I perform the Shapiro's EZW wavelet encoding, transferring the FWT coefficients
	www.wavelet.org /phpBB2/viewtopic.php?p=3307 (539 words)

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