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Topic: Complex Mexican hat wavelet

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	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 PART III by ROBI POLIKAR (Site not responding. Last check: 2007-10-13)
		The wavelet analysis is done in a similar way to the STFT analysis, in the sense that the signal is multiplied with a function, {\it the wavelet}, similar to the window function in the STFT, and the transform is computed separately for different segments of the time-domain signal.
		The mother wavelet is chosen to serve as a prototype for all windows in the process.
		The Morlet wavelet and the Mexican hat function are two candidates, and they are used for the wavelet analysis of the examples which are presented later in this chapter.
	www.site.uottawa.ca /~qingchen/wavelet/p3.htm (5076 words)

	Continuous Wavelet Transform (Site not responding. Last check: 2007-10-13)
		Wavelet Filtering and Reconstruction option offers the means to reconstruct signals from spectral components that have been isolated in the time-frequency domain.
		For the FFT fast convolution to be free of wraparound effects that arise as a consequence of non-periodicity in both the data and the response function (daughter wavelet), zero padding is needed equal to the half the length of the non-zero elements in the daughter wavelet's frequency response.
		The wavelet critical limit gradients are the following colors by default: 8-level grayscale from 10 to 50%, 8-level cyanscale from 50% to 90%, 8-level greenscale from 90% to 95%, 8-level yellowscale from 95% to 99%, and 8-level redscale from 99% to 99.9%.
	www.seasolve.com /products/autosignal/resources/htmlHelp/cont0040.html (3571 words)

	Advanced Concepts (Wavelet Toolbox)
		Wavelets are tools used to study regularity and to conduct local studies.
		Selecting a regularity and a wavelet for the regularity is useful in estimations of the local properties of functions or signals.
		From a theoretical viewpoint, wavelets are used to characterize large sets of mathematical functions and are used in the study of operators linked to partial differential equations.
	www.cs.berkeley.edu /titan/sww/software/matlab/toolbox/wavelet/ch06_a26.html (1653 words)

	The Wavelet Digest :: View topic - Preprint: "Low-Oscillation Complex Wavelets" by P.S. Addison, J.N. Watson ...
		These wavelets, which have been largely ignored to date in the scientific literature, allow for a decomposition which is more 'temporal than spectral' in wavelet space.
		Wavelet transform-based methods employing these wavelets (based on both wavelet ridges and modulus maxima) are developed and applied to sonic echo NDT signals used for the analysis of structural elements.
		Their possible application to two such problems is discussed briefly - the interrogation of arrhythmic ECG signals and the detection and characterisation of coherent structures in turbulent flow fields.
	www.wavelet.org /phpBB2/viewtopic.php?t=5573 (323 words)

	Computational Toolsmiths WavBox Page
		It shows the most famous Daubechies wavelets (those corresponding to filters with four coefficients) and the characteristic tiling of the time-frequency plane with tall thin tiles at high frequencies and short fat tiles at low frequencies.
		Note that the nonsubsampled wavelet transform is an oversampled transform with the same number of data points in each level of the transform domain as in the signal domain.
		However, the discrete wavelet transform is a critically sampled transform with same number of data points in both signal and transform domains because the number of data points is halved at each level in the transform domain.
	www.toolsmiths.com /p/wavbox.aspx (1406 words)

	Fundamentals of the Wavelet Transform Theory - BaseGroup Labs
		Wavelets are extensively used for the purposes of filtration and preprocessing data, analysis and prediction of stock markets situations, image recognition, as well as for processing and synthesizing various signals, like speech or medical signals, for images compressing and processing, training neural networks and so on.
		The idea of using wavelets for the MRA is that the signal is expanded by the basis formed with the offsets and non-uniformly scaled copies of the function prototype (which means that wavelet transform is essentially fractal).
		Besides, the larger is the scale of the wavelet the wider portion of the signal influences the result of the convolution.
	www.basegroup.ru /filtration/intro-to-wavelets.en.htm (1762 words)

	[No title]
		Wavelet Power Like the Fourier transform the wavelet transform is in general complex and is often characterized in terms of it’s power and phase—identically as we’ve seen in the cross-spectral analysis.
		The Mexican hat is a narrow window — compared to the Morlet—and thus we see a finer (broader) temporal (frequency) resolution of its wavelet then the Morlet.
		Wavelet Scale and Fourier Frequency The peak of the wavelet spectrum does not occur at the same peak frequency of the Fourier transform (in figure 2 it should be 1).
	marine.rutgers.edu /dmcs/ms615/2006/Wavelet_Analysis.doc (1692 words)

	Springer Online Reference Works
		A wavelet is, roughly speaking, a (wave-like) function that is well localized in both time and frequency.
		The early vigorous development of wavelet theory is mainly associated with the names of J.
		Wavelets seem particularly suitable to analyze and detect various properties of signals, functions and images, such as discontinuities and fractal structures.
	eom.springer.de /w/w097160.htm (334 words)

	1D Transforms :
		Morlet, Mexican hat, and French hat wavelet transforms are non-dyadic (the resolution is not decreased by a factor two between two scales), and 12 voices (fixed value) are calculated (instead of one for the dyadic case) when the resolution is divided by two.
		Four transforms are non-redundant: the bi-orthogonal, the lifting scheme, and the wavelet packet methods (transforms 17 and 18).
		Continuous wavelet transform with a complex wavelet which can be decomposed into two parts, one for the real part, and the other for the imaginary part:
	www.multiresolution.com /transf1.htm (280 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 Digest, Volume 7, Issue 5 (May 26, 1998)
		The locations of the wavelet atoms and the magnitudes of their coefficients are chosen with respect to a certain marked Poisson process model, allowing intuitive notions about the functions genuinely to be modelled.
		The wavelet packet expansion exploits factorized non-separable very fast filters, and is faster by a factor of 4 than a regular convolution and decimation of the image with separable one-dimensional filters.
		Wavelet research at NASA Dryden concentrates on algorithms to generate time-frequency multiscale representations to identify nonlinear and time-varying aspects of the system dynamics.
	cm.bell-labs.com /wavelet/digest_07/digest_07.05.html (7064 words)

	Systat Software Inc. - AutoSignal - HTML Help
		The CWT is a convolution of the data sequence with a scaled and translated version of the mother wavelet, the
		wavelet's resolution in frequency at its best (order 40) is close to the Morlet with its least wavenumber of 6.
		The critical limits are based on Monte Carlo trials where a large number of white noise sets were analyzed to determine variance-normalized CWT spectral maxima as a function of data set size, wavelet, wavelet adjustable parameter, and real/complex state of the wavelet.
	www.systat.com /products/AutoSignal/help/?sec=1102 (3497 words)

	Morlet wavelet and transform (Site not responding. Last check: 2007-10-13)
		Although the discrete Haar wavelets predate Morlet's, it was only as a consequence of Morlet's work that the mathematical foundations of wavelets as a better formulation of time-frequency methods were laid.
		Conceptually related to windowed-Fourier analysis, the Morlet wavelet is a locally periodic wavetrain.
		Clearly, the wavelet transform will have a real and an imaginary part, and it is useful to represent them in `polar' coordinates: the norm is the magnitude of the transform and, being related to the local energy, is of primary interest, while the polar angle (phase) completes the representation.
	www.ecs.syr.edu /faculty/lewalle/tutor/node14.html (261 words)

	WAVELETS
		Getting into the complex wavelet domain was easy compared to returning back to the ``time'' domain.
		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.
	www.isye.gatech.edu /~brani/wavelet.html (3093 words)

	Tools for fractal analysis (Site not responding. Last check: 2007-10-13)
		The wavelet transform of x is computed via convolutions of dilated and translated versions of a single function called the "mother wavelet".
		After convolution of the mirrored signal with the analyzing wavelet, the result is truncated to the actual size of the initial signal.
		The reconstruction algorithm Inverse Wavelet Transform, proceeds by convolving the wavelet coefficients (obtained from contwt) by the synthesis wavelet.
	pauillac.inria.fr /cdrom/www/scilab/doc/manual/docu019.html (9532 words)

	The Wavelet Digest, Volume 5, Issue 9 (November 4, 1996)
		Requirements for the wavelet position include a Ph.D. thesis in the general area of wavelet transforms, an interest in developing new computational methods, significant experience in developing or analyzing computer algorithms, a strong mathematical background, an interest in physics, and an interest in applying theoretical knowledge to practical problems.
		Matthias Holschneider (hols@titan.univ-rennes1.fr) informed me that the traveling wavelets method is due to M. Holschneider, V. Perrier, and C. Basdevant, and that the first paper about this appears "in the CRAS." The paper from which I learned about the method is: V. Perrier and C. Basdevant, `Travelling Wavelets Method', Proc.
		We are working on low complexity adaptive beamforming and we studied application of wavelet filters in generalized sidelobe canceller's blocking matrix in order to obtain faster convergence of the adaptive algorithms with a resonable computation load.
	cm.bell-labs.com /cm/ms/what/wavelet/digest_05/digest_05.09.html (4068 words)

	Advanced Concepts (Wavelet Toolbox)
		There are different types of wavelet families whose qualities vary according to several criteria.
		Some are given explicitly by their time definitions, others by their frequency definitions, and still others by their filters.
		The table below outlines the wavelet families included in the toolbox.
	www.technion.ac.il /guides/matlab/toolbox/wavelet/ch06_a27.html (169 words)

	X-Ray Source Detection Using the Wavelet Transform
		We use an iterative approach to correlate data with the Mexican Hat function and to cleanse suspected sources from the data.
		The wavelet transform is a powerful new tool for the detection of astronomical sources (Slezak, Bijaoui, and Mars 1990; Rosati et al.
		The wavelet function most used for source detection is the Mexican Hat (MH) function, which in its rotationally-symmetric form is proportional to the second derivative of a two-dimensional symmetric Gaussian function of width
	iraf.noao.edu /iraf/web/iraf/ftp/ftp/conf/web/adass_proc/adass_95/freemanp/freemanp.html (1146 words)

	Wavelet Toolbox: Table of Contents (Wavelet Toolbox)
		Summary of Wavelet Families and Associated Properties (Part 1)
		From Wavelets to Wavelet Packets: Decomposing the Details
		Wavelet Packet Tool Features (1-D and 2-D) Node Action Functionality
	www.socsci.umn.edu /ssrf/doc/matlab/toolbox/wavelet/wavbookt.html (274 words)

	[No title]
		2-D wavelet analysis and 2-D stationary wavelet analysis
		Load data for Stochastic Design Regression dialog box
		More on Residuals for Wavelet 1-D Compression window
	www.weizmann.ac.il /matlab/toolbox/wavelet/waveletindex.xml (24 words)

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