Wavelet-технологии

Mathcad Wavelets Extension PackСовременный мощный набор вейвлет-функций Дополнительный пакет Mathcad Wavelets Extension Pack предоставляет

bl0nd1nka — Fri, 27 Apr 2012 20:04:04 GMT

Современный мощный набор вейвлет-функций

Дополнительный пакет Mathcad Wavelets Extension Pack предоставляет новые средства для анализа сигналов и изображений, анализа временных рядов, статистической оценки сигнала, анализа сжатия данных и специальных численных методов. Новые возможности позволяют создавать практически неограниченное число функций, с помощью которых можно воспроизводить естественную или абстрактную среду. Новая функциональность включает одно- и двумерные волновые преобразования (вейвлет-функции), дискретные волновые преобразования, анализ сжатия растровых изображений и многое другое.

Вейвлет-анализ (или анализ всплесков) является эффективным инструментом обработки сигналов различной природы и находит применение в математике, физике, астрономии, медицине, радиоэлектронике и других областях. Новые вейвлет-функции обеспечивают более действенные и результативные методы по сравнению с традиционными методами, например, основанными на дискретных преобразованиях Фурье.
Модуль Wavelets Extension Pack содержит более 60 базовых вейвлет-функций, составляя сильную конкуренцию аналогичным средствам MATLAB и Mathematica и имея более доступную рыночную цену. Широкий диапазон ортогональных и биортогональных семейств вейвлетов включает вейвлеты Хаара, Добеши, Койфмана, симмлеты, а также B-сплайны.
Популярный интерфейс Mathcad обеспечивает высокую лёгкость и скорость работы. Гибкая универсальная среда Mathcad идеально подходит для экспериментирования с вейвлетами и выполнения тестовых задач в стиле «что-если». Wavelets Extension Pack отлично интегрирован с Mathcad и другими дополнительными пакетами (включая Signal Processing и Image Processing Extension Packs), значительно расширяя возможности пользователя.

Продукт Mathcad Wavelets Extension Pack сопровождается большим объёмом интерактивной документации по основам вейвлетов и приложениям с примерами и справочными таблицами.

Источник: PTS - продуктивные технологические системы

Немного полезных сайтов

Mby-Sci — Thu, 26 Apr 2012 16:08:07 GMT

ВЕЙВЛЕТЫ И НЕЙРОННЫЕ СЕТИ

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A WAVELET-BASED TECHNIQUE TO DECREASE FULL-WAVE SIMULATION TIME OF MICRO WAVE/M M-WAVE TRANSISTORS

Mby-Sci — Wed, 25 Apr 2012 19:30:50 GMT

Masoud Movahhedi, AbdolAli Abdipour Microwave/mm-wave & Wireless communication research Lab., Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran E-mail: Movahhedi@aut.ac.ir, Abdipour@aut.ac.ir

Abstract – A new wavelet-based simulation approach for the analysis and simulation of microwave/mm-wave transistors is presented. For the first time in the literature, Daubechies-base wavelet approach is applied to semiconductor equations to generate a nonuniform mesh. This allows forming fine and coarse grids in locations where variable solutions change rapidly and slowly, respectively. The procedure of nonuniform mesh generation is described in details by simulating a MESFET. It is shown that good accuracy can be achieved while compressing the number of unknown by 70%.’

Index Terms – full-wave analysis, nonuniform wavelet-base grid, transistor simulation, Daubechies-based wavelet.

I. Introduction

Recent progress in microwave technology over the past decade led to the development of smaller devices for higher operating frequencies. As the frequency increases, electromagnetic effect occurring inside the transistor cannot be neglected. Phenomena such as the phase velocity mismatch between gate and drain modes and reflection from electrodes open ends, affects the propagation of the wave along the device structure and therefore affects the device performance. Circuit-based models, distributed and semi-distributed models, usually used suffer from poor simulation of the EM wave propagation and questionable validity of the wave device interaction taking place inside the transistor [1]. The full- wave physical analysis of semiconductor devices is based on the coupling of Maxwell’s equations and the semiconductor equations used to characterize the dynamic of the electron inside the device [1]. After having an accurate device simulation approach, the characterization and full-wave analysis of microwave circuits included active and passive devices, is important. Therefore, the circuit analysis should be based on the advanced global model, which takes the electromagnetic (EM) wave effects into considerations. In the global modeling technique, the active devices are simulated by combining the electron transport and the EM models and the passive devices are simulated using the EM model [2].

The full-wave analysis of microwave and millimeter- wave transistors and global modeling of microwave circuits are a tremendous task that requires involved advanced numerical techniques and different algorithms

[3] . As a result, it is computationally expensive. Therefore, there is an urgent need to present a new approach to reduce the simulation time, while maintaining the same degree of accuracy. A conventional numerical approach to solve the differential equations of active part (transistors) and Maxwell’s equations for both passive and active parts is Finite-Difference Time-Domain (FDTD) technique. In this method, the unknown parameters are calculated in discrete positions named mesh nodes. By implementation a technique for generation a nonuniform mesh, we would considerably reduce the number of unknowns and also decrease the time of simulation and analysis. In this

This work has been supported in part by Iran Telecommunication Research Center (ITRS).

nonuniform mesh, the density of nodes in domains where the unknown quantities vary rapidly is higher than the other regions. Such a technique corresponds to a multiresolution of the problem. A very attractive way of implementing a multi-resolution analysis is to use wavelets [4]. Wavelets have been used in electromagnetics for a few years, first in the method of moments, and later in FDTD [5]. One of the approaches for solving Partial Differential Equations (PDEs) is the interpolating wavelets technique which has been applied to the drift-diffusion [6] and full hydrodynamic active device model [7].

In this paper, we propose to generate a nonuniform grid [8] for simulating of microwave transistors using Daubechies-based wavelet method. The transistor first is biased and steady-state parameter solutions are obtained using FDTD and uniform grid. Then, the proposed wavelet scheme is applied to the solutions and a nonuniform grid is generated. This mesh can be used in ac excitation state and decreases the time of full-wave simulation, significantly.

II.Daubechies-Based Wavelet Scheme

In the numerical simulation of equations it is common that small scale structure will exist in only a small percentage of the domain. If one chooses a uniform numerical grid fine enough to resolve the small scale features in the majority of the domain the solution to the equations will be over resolved. One would like, ideally, to have a dense grid where small scale structure exists and a sparse grid where the solution is composed only of large scale features. Now we consider a Daubechies-based wavelet system. Wavelets provide a natural mechanism for decomposing a solution into a set of coefficients which depend on scale and location. One can then work with the solution in a compressed form where one works only with the wavelet coefficients which are larger in magnitude than a given threshold. Wavelets, therefore, sound ideal for solving the type of problem mentioned previously

[8] .The idea of using wavelets to generate numerical grids began with the observation in [9] that the essence of an adaptive wavelet-Galerkin method is nothing more than a finite difference method with grid refinement. Jameson demonstrated in [8] that Daubechies wavelet expansion represents a localized mesh refinement. In this paper we will follow his wavelet based grid generation algorithm explained in [10].

III. Transistor Physical Model

The semiconductor models used are based on the moments of Boltzmann’s transport equations obtained by integration over the momentum space. Three equations need to be solved together with Poisson’s equation in order to get the quasi-static characteristics of the transistor. This system of coupled highly nonlinear partial differential equations contains current continuity, energy conservation and momentum conservation equations [11]. The solution of this system of partial differential equations represents the complete hydrodynamic model. Simplified models are obtained neglecting some terms in momentum equation. One of these simplified models is drift-diffusion model (DDM). In this paper we simulate MESFET as microwave/mm transistor that is a unipolar device. For this device, the equations to be solved in the drift-diffusion model are: Poisson’s equation:

where® is potential, N is the doping profile, n is the electron (carrier) density, and /лп and D„ are the mobility and the diffusion coefficient, respectively. In this work, electron mobility has been considered as a function of doping and electric field:

The parameters of this equation have been defined in [12]. The diffusivity is defined by the Einstein relation D = kt/q/u.In order to characterize wave propagation-

device interaction inside the transistor, the electromagnetic and the semiconductor model must be coupled. The full-wave analysis and simulation start by obtaining the steady-state dc solution, using Poisson’s equation and the semiconductor device model. The dc solution is used in the ac analysis as initial values. Then the ac excitation is applied. Maxwell’s equations are solved for the electric and magnetic field distributions. The new fields are used in the semiconductor model to find the current density. This process is repeated for each time interval [1]. We use FDTD technique to solve the equations and achieve stable and accurate solutions. At the first, a uniform mesh that covers the 2-D cross section of the MESFET is used. Initially, the device is biased and the dc parameter distributions (potential and carrier density) are obtained by solving the drift-diffusion model only. After calculating the distributions of these parameters, we apply wavelet scheme to the solutions and determine where quantities vary rapidly and slowly. In domains that the variation of parameters is low, the wavelet method can refine the mesh and reduce the nodes of initial uniform mesh. By this method, we can generate a nonuniform mesh that its density is low in dispensable places. Because the dc solution is used in ac analysis as initial values and also the level of ac excitation is lower than dc level at most times, therefore one can conclude after applying ac excitation to the structure, the distributions of parameters will fix approximately. For this reason, we can use the nonuniform mesh generated from dc solution in ac analysis.

IV. Simulation Results

The approach presented in this paper is general and can be applied to any transistor. The transistor considered in this simulation is a 0.6-|im gate MESFET with the following dimensions and parameters: 1-|im-long source and drain electrodes, 0.7-|im source-gate gap, 1.5-цт gate drain separation, 0.2-|im-deep channel layer, and a

0. 8-|im-deep buffer or semi-insulating layer. Fig. 1 presents the conventional 2-D structure used for simulation. The doping of active layer is 1.2×1017 A/cm3 and the doping of the buffer layer is 1 x 1014 A/cm3. An 133 Дх x 33 Ay uniform mesh that covers the 2-D structure is used. Forward Euler is adopted as an explicit FD method to discretize drift-diffusion equations and Scharfetter- Gummel approximation [11] is used to determine the current density on the mid-points of the mesh. The device is biased to Vds = 2.0V and Vgs = -1V and the dc distributions of parameters are obtained by solving the physical model equations. The state of the MESFET under dc steady-state is represented by the distribution of potential and carrier density. Now, the mentioned wavelet approach is applied to each parameter (potential and carrier density) and then solutions are combined together to generate final nonuniform grid. Fig. 2 shows the procedure employed to obtain the nonuniform grid of the carrier density. The carrier density obtained from dc analysis is a function of x and y, n(x,y). The proposed wavelet scheme first, applies to the longitudinal cross sections, n(x), and removes some grids (Fig. 2(a)) and then applied to the transverse cross section, n(y), (Fig. 2(b)). The process is achieved by obtaining two separate grids for the transverse and longitudinal compressions. The two grids are then combined together using logical "AND” to conceive the overall grid for the carrier density (Fig. 2(c)). It should be observed that the proposed technique accurately removes grid point in the locations where variable solutions change very slowly (Fig. 2(d)). The same process is conducted for the other variable, potential. Fig. 3(a) shows the final grid for the potential after applying wavelet scheme. Because the variation of potential is slow, therefore the number of potential mesh nodes is smaller than the number of carrier density mesh nodes.

The separate grids of our variables are then combined using logical "OR” to obtain the overall grid for the cross section of MESFET (Fig. 3(b)). Considering the overall grid given by Fig. 3(b), the number of nodes after adding the necessary grid points is 1322, that shows about 70% compression for uniform mesh. The value of compression of algorithm depends on the threshold parameter defined in proposed wavelet scheme. In this simulation, threshold value has been set to 0.00008 for normalized quantities. One must trade off between the simulation time and solution accuracy to select the threshold value or level of compression. Now, this nonuniform mesh can be used to analyze the transistor when the ac excitation is applied. With this assumption that the level of ac excitation is lower than dc bias, the parameters distribution will be unchanged, approximately, and this nonuniform mesh will be valid. To evaluate of proposed method and generated nonuniform mesh, we added a gate voltage, Avgs = 0.1V, to the previous bias point and calculated drain current. The difference between the solutions, when uniform mesh and nonuniform mesh are used, equal to 2.9% that shows the accuracy of generated nonuniform mesh.

V. Conclusion

A wavelet approach based on the Daubechies wavelet scheme has been used to generate a nonuniform mesh toward full-wave analysis of microwave/mm-wave transistors. A reduction of 70% in the number of nodes is obtained while keeping drain current in an acceptable 2.9% of accuracy with the initial uniform mesh. This opens the door to an efficient numerical technique suitable for global modeling of microwave circuits.

[1]M. A. Alsunaidi, S. M. S. Imtiaz, and S. M. El-Ghazaly, "Electro-magnetic wave effects on microwave transistors using a full-wave high-frequency time-domain model,” IEEE Trans. Microwave Theory Tech, vol. 44, pp. 799-808, June1996.

[2]S. M. Sohel Imtiaz and S. M. El-Ghazaly, "Global modeling of millimeter-wave circuits: Electromagnetics simulation of amplifiers,” IEEE Trans. Microwave Theory Tech, vol. 45, pp. 2208-2216, Dec. 1997.

[3]R. O. Grondin, S. M. El-Ghazaly, and S. Goodnick, "A review of global modeling of charge transport in semiconductors and full-wave electromagnetics,” IEEE Trans. Microwave Theory Tech., vol. 47, pp. 817-829, June 1999.

[4]S. G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Patt. Anal. Machine Intel!., vol. 11, pp. 674-693, July 1989.

[5]B. Z. Steinberg and Y. Leviatan, "On the use of wavelet expansions in the method of moments, "IEEE Trans. Antennas Propagat., vol. 41, pp. 610-619, May 1993.

[6]S. Goasguen, М. M. Tomeh, and S. M. El-Ghazaly, "Electromagnetic and semiconductor device simulation using interpolating wavelets,” IEEE Trans. Microwave Theory Tech., vol. 49, pp. 2258-2265, December 2001.

[7] Y. A. Hussein, and S. M. El-Ghazaly, "Extending multiresolution time-domain (MRTD) technique to the simulation of high-frequency active devices,” IEEE Trans. Microwave Theory Tech., vol. 51, pp. 1842-1851, July 2003.

[8] L. Jameson, "On the wavelet optimized Finite Difference method,” ICASE Report, No. 94-9, NASA Langley Research Center, Hampton, 1994.

[9] L. Jameson, "On the differentiation matrix for Daubechies- based wavelets on an interval,” ICASE Report, No. 93-94, NASA Langley Research Center, Hampton, 1993.

[10]L. Jameson, "Wavelet-based grid generation,” ICASE Report, No. 96-31, NASA Langley Research Center, Hampton, 1996.

[11 ] Y. K. Feng and A. Hintz, "Simulation of submicrometer GaAs MESFET Susing a full dynamic transport model,”

IEEE Trans. Electron Devices, vol. 35, pp. 1419-1431, Sept. 1988.

[12] X. Zhou and H. S. Tan, "Monte carlo formulation of field- dependent mobility for AlxGa^xAs,” Solid-State Electronics, vol. 38, pp. 567-569, 1994.

Fig. 1. 2-D conventional structure of the simulated MESFET

Fig. 2. (a) Compression for the carrier density at the longitudinal cross sections, (b) Compression for the carrier density at the transverse cross sections, (c) Final grid for the carrier density, (d) Normalized carrier density contour plot (n/Noi).

Источник: Материалы Международной Крымской конференции «СВЧ-техника и телекоммуникационные технологии»

Wavelet libraries

Mby-Sci — Tue, 10 Apr 2012 18:19:50 GMT

Fourier Analysis - Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to Fourier analysis, which studies approximations and decompositions of functions using trigonometric polynomials. Of incalculable value in many applications of analysis, this field has grown to include many specific and powerful results, including convergence criteria, estimates and inequalities, and existence and uniqueness results. Extensions include the theory of singular integrals, Fourier transforms, and the study of the appropriate function spaces. Also approximations by other orthogonal families of functions, including orthogonal polynomials and wavelets. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>>

An Introduction to Fourier Theory - Forrest Hoffman
A paper about Fourier transformations, which decompose or separate a waveform or function into sinusoids of different frequencies that sum to the original waveform. Fourier theory is an important tool in science and engineering. Contents: Introduction; The Fourier Transform; The Two Domains; Fourier Transform Properties - Scaling Property, Shifting Property, Convolution Theorem, Correlation Theorem; Parseval's Theorem; Sampling Theorem; Aliasing; Discrete Fourier Transform (DFT); Fast Fourier Transform (FFT); Summary; References. more>>

An Introduction to Wavelets - Amara Graps; Institute of Electrical and Electronics Engineers, Inc.
A paper giving an overview of wavelets: mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. Wavelets have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. This paper include information about signal processing algorithms, Orthogonal Basis Functions, and wavelet applications. more>>

Wavelet Digest: wavelet.org - Wim Sweldens
A free monthly newsletter with all kinds of information concerning wavelets; announcement of conferences, preprints, software, questions, etc. The latest issue and searchable copies of back issues (beginning in 1992) are available; links to other wavelet sites are provided. more>>

Wavelets - Salzburg, Austria
An extensive list of links to Internet sources of information for wavelets, and some bibliographies. more>>

The Wavelet Tutorial - Robi Polikar
The engineer's ultimate guide to wavelet analysis: a tutorial that explains basics of signal processing with a focus on the technique of wavelet transformations (WT). Basic concepts of importance in understanding wavelet theory; Short Term Fourier Transform (STFT) (used to obtain time-frequency representations of non-stationary signals); continuous wavelet transform (CWT) (how problems inherent to the STFT are solved); discrete wavelet transform (a very effective and fast technique to compute the WT of a signal). Bibliography included. more>>

More information at The Math Forum

Wavelet Software

Mby-Sci — Tue, 10 Apr 2012 18:15:33 GMT

Wavelet Software

The amount of wavelets-related software is multiplying!

The "Bath Wavelet Warehouse"

Here is a repository of wavelet filters for you to download and use. The wavelet file (.wvf), uses an easy to understand format to describe wavelet filter coefficients. Included are filters for Biorthogonal wavelets: Bath wavelets ('Bathlets'), UCLA evaluated wavelets, fingerprint wavelets, modified Coiflet filters; Orthonormal wavelets: Bath wavelets, Complex Bathlets, Haar wavelet, Daubechie's wavelets, wavelets to reduce coding artifacts, and other miscellaneous wavelets.
The Bath Wavelet Warehouse.

"WaveLab" at Stanford University

David Donoho and coworkers in the Stanford Statistics Department have made publicly available: WaveLab .802, a library of Matlab routines for wavelet analysis, wavelet-packet analysis, cosine-packet analysis and matching pursuit. The library, provided for machines that can run Matlab5.x is available free of charge over the Internet. WaveLab currently has over 900 files consisting of scripts, M-files, MEX-files, datasets, self- running demonstrations, and on-line documentation. It been used in teaching courses in adapted wavelet analysis at Stanford and at Berkeley, and is the basis for wavelet research by the authors.
WaveLab Matlab Software.

"PiefLab" by Maarten Jansen

PiefLab is a library of Matlab algorithms for wavelet noise reduction PiefLab has several routines for: 1) Wavelet transforms: fast and undecimated, (bi)orthogonal, 1D, 2D. Special attention was paid to fast implementation through Matlab blass routines and polyphase implementation of filter banks. 2) Noise reduction by wavelet thresholding, including threshold assessment by minimum MSE, minimum SURE, minimum GCV. 3) Bayesian correction of threshold selections for images (and other 2D structers) using a geometrical prior. 4) CVS - Conditional Variance Stabilisation for Poisson intensities, including a Bayesian model within this framework. It also includes routines for Fisz-wavelet transforms (Fryzlewicz, Nason). Some of the test routines require that you download software from Theofanis Sapatinas' collection of Poisson Wavelet Denoising Software. PiefLab runs without any additional toolbox. It can be integrated into WaveLab, but it also stands on its own, i.e. it provides its own procedures for wavelet transforms.
PiefLab Matlab Software.

"WavBox" Software by WavBox ToolSmiths

A full-featured Matlab (GUI and command-line) toolbox by Carl Taswell for performing wavelet transforms and adaptive wavelet packet decompositions. WavBox contains a collection of wavelet transforms, decompositions, and related functions that perform multiresolution analyses of 1-D multichannel signals and 2-D images. The older version 4.1 includes overscaled pyramid transforms, discrete wavelet transforms, and adaptive wavelet and cosine packet decompositions by best basis and matching pursuit as described by Mallat, Coifman, Wickerhauser, and other authors, as well as Donoho and Johnstone's wavelet shrinkage denoising methods. The new version 4.2 does the above plus it implements Taswell's satisficing search algorithms for the selection of near-best basis decompositions with either additive or non-additive information costs. The new version also includes the continuous wavelet transform valid for all wavelets including the complex Morlet, real Gabor, and Mexican hat wavelets. Versions 1-3 are in the public domain. Versions later than this are commercial.
Wavbox by WavBox ToolSmiths.

"The MATLAB Wavelet Toolbox" by The MathWorks

A full-featured MATLAB (GUI and command-line) toolbox written by Michel Misiti, Yves Misiti, Georges Oppenheim and Jean-Michel Poggi, of the Laboratoire de Mathematiques, Orsay-Paris 11 University, France. The MATLAB Wavelet Toolbox contains continuous wavelet transforms (CWT), 1D and 2D discrete wavelet transforms (DWT), multiresolution decomposition and analysis of signals and images, user-extensible selection of wavelet basis functions, 1D and 2D wavelet packet transforms, entropy-based wavelet packet tree pruning for "best-tree" and "best-level" analysis, and soft and hard thresholding De-noising. Bundled with the Wavelet Toolbox is the new book, "Wavelets and Filter Banks", by Gilbert Strang and Truong Nguyen. Many exercises in this book are drawn from the toolbox.
The MATLAB Wavelet Toolbox by The MathWorks. and Making Wavelets in Finance (article describing application of Toolbox).

Discrete Periodic Wavelet Transform Matlab Software

Neil Getz has written some papers, code and a web page describing the discrete periodic wavelet transform. This is a collection of Matlab routines designed to enable easy experimentation with the DPWT and its inverse. Some knowledge of the background material contained in the attached two publications is suggested.
Discrete Periodic Wavelet Transform Matlab Software.

"Time-Frequency Toolbox" for Matlab by Auger, Lemoine, Goncalves and Flandrin.

This free (copyrighted) software is is a collection of about 100 M-files, developed for the analysis of non-stationary signals using time-frequency distributions. It performs signal generation files, processing and post-processing (including visualization). The toolbox is primary intended for researchers and engineers with some basic knowledge in signal processing. It requires at least Matlab v4.2c (or later version) and the Signal Processing Toolbox, v3.0 or later.
The Time-Frequency Toolbox.

The "WMTSA" Wavelet Toolkit for Matlab by Percival and Walden.

This is a software package for the analysis of a data series using wavelet methods. КIt is an implementation of the wavelet-based techniques for the analysis of time series presented in: Wavelet Methods for Time Series Analysis. The WMTSA toolkit consists of: 1) the WMTSA MATLAB toolbox containing functions for computing several versions of the discrete wavelet transform (DWT), analyzing variability as a function of scale, displaying results and 2) example scripts and data demonstrating use of the toolbox and 3) documentation of toolbox functions.
The WMTSA Wavelet Toolkit.

"Image Fusion" Matlab Toolbox from Oliver Rockinger

This Matlab package from The image fusion toolbox for matlab 5.x comprises a set of m-file functions for the pixel-level image fusion of spatially registered grayscale images. It is accompanied by an easy-to-use graphical interface which allows an interactive control over all relevant parameters. .
Image Fusion Toolbox

"Wavekit" from Harri Ojanen

This is a wavelet toolbox for Matlab 5.1-greater geared mostly towards learning about wavelets from the author's own explorations. It includes one- and two-dimensional (periodic) fast wavelet and wavelet packet transforms and the best basis algorithm for wavelet packets, an implementation of the fast matrix multiplication algorithm of Beylkin, Coifman, and Rokhlin (Comm. Pure Applied Math 44(2), 1991) for both wavelets and wavelet packets, and various demonstrations on visualizing wavelets and signal analysis.
Wavekit by Harri Ojanen.

"Multiwavelet" package from Vasily Strela

This is a wavelet toolbox for Matlab 5.1 with the aim to give researchers an opportunity to try multiwavelets in practice. MWMP can be used for comparison of scalar and multiple filters in image compression and signal denoising. MWMP offers a variety of builtin scalar- and multi- filters. Several types of prefilters are included. New sets of coefficients can be easily added. In addition to routines implementing preprocessing and discrete multiwavelet transform (in 1 and 2 dimensions) the package contains a simple compression function and several scripts for signal denoising via thresholding. All routines in MWMP include a help section explaining input and output parameters and giving example of usage.
Multiwavelet by Vasily Strela.

The Rice Wavelet Toolbox Release 2.4

The Rice Wavelet Toolbox Release 2.4 is a collection of MATLAB of "mfiles" and "mex" files for twoband and M-band filter bank/wavelet analysis from the DSP group and Computational Mathematics Laboratory (CML) at Rice University, Houston, TX. This release includes application code for Synthetic Aperture Radar despeckling and for deblocking of JPEG decompressed Images. In addition: more wavelet and DSP software can be found at: http://www-dsp.rice.edu/software.
Matlab Rice Wavelet Toolbox.

"TIPSH" Matlab software by Eric Kolaczyk et al.

This TIPSH software performs the method of Translationally Invariant Smoothing of Poisson data using Haar Wavelets. TIPSH is useful for the removal of Poisson noise from count data, or more generally, for non-parametric hypothesis testing of Poisson data. In the latter case, one can non-parametrically extract the statistically significant residual from a dataset given some null hypothesis.
"TIPSH" Matlab software.

The "Uvi_Wave" Wavelet Toolbox.

The Uvi_Wave Wavelet Toolbox is a set of Wavelet Processing based functions implemented under two known environments: Matlab and Khoros 2. The toolbox includes Wavelet Transform functions for one or more dimensions (up to 5 dimensions in Khoros 2). Matlab version also includes Wavelet Packet Transform (one and two dimensional). Multiresolution Analysis functions have been implemented to calculate approximation and detail components of any signal or object. Wavelet Filter Generation routines have been programed so as to generate Daubechie, Symlets and Remez Orthogonal filters as well as Spline Biorthogonal Filters. Matlab version provides additional orthogonal filter families: Maximally Flat and Battle-LemariЋ. The Wavelet and Scaling functions can be computed from any kind of Wavelet Filters.
The Uvi_Wave Wavelet Toolbox .

Wavelet Transform Matlab software by Shihua Cai & Keyong Li.

This is a library of wavelet transform Matlab software for 1D, 2D, and 3D signals. See the web page for more information.
Wavelet Transform Matlab software by Shihua Cai & Keyong Li.

"LISQ" Matlab software by Paul de Zeeuw.

The functions include second generation wavelet decomposition and reconstruction tools for images as well as functions for the computation of moments. The wavelet schemes rely on the lifting scheme of Sweldens and use the splitting of rectangular grids into quincunx grids, also known as red-black ordering. The prediction filters include the Neville filters as well as a nonlinear 'maxmin' filter. The various functions are described and examples are given. The toolbox is provided with appliances for the visualization of data on quincunx grids.
LISQ Matlab software by Paul de Zeeuw

"BLS-GSM" image denoising Matlab code by Javier Portilla et al.

We have just released a Matlab implementation of our algorithms for image denoising (BLS-GSM stands for Bayes Least Squares - Gaussian Scale Mixtures). The method uses a Gaussian Scale Mixture model for neighborhoods of coefficients in the wavelet domain. It works both with the full steerable pyramid and with redundant versions of orthogonal wavelets. It provides state-of-the-art denoising performance at reasonable computational cost. You can find a description of the statistical model, examples of denoised images, links to relevant publications, and the full Matlab source code at the link.
>BLS-GSM image denoising Matlab code by Javier Portilla et al.

"JPEGTools" Matlab and Octave software.

A package of Octave and Matlab scripts has been written to accompany material in the book: Introduction to Information Theory and Data Compression by Darrel Hankerson, Greg A. Harris, and Peter D. Johnson Jr. Documentation appears in Appendix A of the textbook, and is also available in Portable Document Fromat (PDF) as jpegtool.pdf (try jpegtool_compat.pdf if your software complains), or in PostScript form as jpegtool.ps.gz (compressed with gzip). The scripts can be used to study JPEG-like schemes. The scripts are freely-distributable under the GNU General Public License.
>JPEGTools Matlab and Octave software

Wavelet denoing Matlab software by Antoniadis, A. et al.

This software performs wavelet shrinkage and wavelet thresholding estimation.
Wavelet denoising Matlab software.

"IDL Wavelet Toolkit" from Research Systems, Inc.

IDL Wavelet Toolkit, an optional module for IDL version 5.5. It is is a set of graphical user interfaces (GUI) and IDL routines developed specifically for the wavelet analysis of multi-dimensional data. In the IDL Wavelet Toolkit, you will find a set of standard wavelet techniques.
Wavelet Toolkit IDL Software.

"Lastwave" at Centre de Mathematiques Appliquees

Lastwave is signal processing software written by researcher Emmanuel Bacry at Centre de Mathematiques Appliquees, Ecole Polytechnique with contributors: B. Audit, N. Decoster, J.F. Muzy, C. Vaillant, J. Abadia, J. Fraleu, R. Gribonval, J. Kalifa, E. LePennec, S. Mallat, G. Davis, W.L. Hwang, and S. Zhong. He wrote software that is free (GNU License), written in C, and runs on both X11/Unix and Macintosh computers, and should be easy to include one's own code. LastWave is a signal processing (wavelet oriented) software, designed to be used by anybody who knows about signal processing and wants to play around with wavelets and wavelet-like techniques. It mainly consists in a (tcl like) powerful command line language which includes a high level object-oriented graphic language which allows to display both some simple objects (e.g., buttons, strings, text using any font, ...) and some complex objects (signals, images, wavelet transforms, extrema representation, ....). All these graphic objects can be fully controlled (along with the mouse behavior) via the command language. There is full postscript and PDF document available.
Lastwave Software.

Mathematica "Lifting" Notebook by Paul Abbott.

Abbott has placed a Mathematica tutorial Notebook on wavelets via the Lifting algorithm at the following URL, along with an honours thesis by his student Mark Maslen. This Notebook gives some background on factorization of transforms (such as the FFT) and then works through some of the examples in the paper: http://cm.bell-labs.com/who/wim/papers/papers.html#factor by Daubechies and Sweldens which describes a technique which can accelerate wavelet transforms by a factor of two by factoring them in elementary lifting steps.
Mathematica "Lifting" Notebook and Mark Maslen's 1997 Lifting Honours thesis.

Mathematica CWT software by David A. Jay

David A. Jay at the Oregon Graduate Institute has written Mathematica CWT software, free to download. The programs provided in the library are designed to allow the calculation of the time evolution of the frequency content of a signal. These codes were developed to investigate non-stationary tidal processes (e.g., barotropic river tides and continental shelf internal tides) where the astronomically forced tide is so strongly modulated by non-tidal processes that the signal becomes strongly non-stationary.
Mathematica CWT software by David A. Jay.

Mathematica wavelet programs

This directory at the Colorado School of Mines contains a series of Mathematica programs designed to display the features and properties of various types of wavelets. There are also PostScript files documenting the programs as well as some additional documents about wavelets.
Mathematica wavelet programs.

"Wavelet Explorer" from Wolfram Research

This Mathematica package from Wolfram Research offers a thorough tutorial for those new to wavelet theory as well as provides a complete set of tools for advanced wavelet research. Wavelet Explorer generates a variety of orthogonal and biorthogonal filters and computes scaling functions, wavelets, and wavelet packets from a given filter. It also contains 1D and 2D wavelet and wavelet packet transforms, 1D and 2D local trigonometric transforms and packet transforms, and it performs multiresolution decomposition as well as 1D and 2D data compression and denoising tasks. Graphics utilities are provided to allow the user to visualize the results. It is written entirely in Mathematica with all source code open, so that the user is free to customize and extend all of the functions.
Wavelet Explorer by Wolfram Research.

Maple "CBC" programs from Bin Han

Maple routines have been developed to construct 1-dimensional and 2-dimensional Hermite interpolatory matrix masks and pairs of biorthogonal matrix masks with a general dilation matrix using the CBC (Coset By Coset) algorithm. By calling several routines from these programs, you can easily construct 1D/2D biorthogonal multiwavelets with a general dilation matrix using the CBC algorithms. You can also find C programs (calling MATLAB routine eig) to compute smoothness of a symmetric refinable function in 1D/2D/3D using symmetry.
Maple CBC programs from Bin Han.

"WAILI" C++ Wavelet Transform Library by Uytterhoeven, Wulpen, Jansen.

Geert Uytterhoeven, Filip Van Wulpen, Maarten Jansen have written a wavelet transform library. It includes some basic image processing operations based on the use of wavelets and forms the backbone of more complex image processing operations. It uses integer wavelet transforms based on the Lifting Scheme, provides various wavelet transforms of the Cohen-Daubechies-Feauveau family of biorthogonal wavelets, provides crop and merge operations on wavelet-transformed images, provides noise reduction based on wavelet thresholding, and provides scaling, edge enhancement of images. WAILI is available in source form for research purposes only and may not be further distributed. Enquiries about the license conditions should be directed to wavelets@cs.kuleuven.ac.be.
"WAILI" C++ Wavelet Transform Library

"Wave++" from the Ryerson Computational Signal Analysis Group

TWave++ is a C++ library of classes and functions designed for the serious programmer wishing to write software or scientific applications which employ the elements of wavelet analysis, time-frequency analysis or Fourier analysis. Wave++ is a carefully designed, thoroughly tested portable library of reuseable, extensible algorithms and data structures which allow the user to write efficient, fast executing programs in a wide spectrum of signal processing and data analysis applications.
Wave++ library.

"ImageLib" C++ library from Brendt Wohlberg

ImageLib is a C++ class library providing image processing and related facilities. The main set of classes provide a variety of image and vector types, with additional modules supporting scalar and vector quantisation, DCT transforms and wavelet transforms. Periodic and symmetric extension wavelet transforms are provided, as well as facilities for plotting scaling functions, wavelets, and wavelet filter frequency responses.
ImageLib C++ library from Brendt Wohlberg.

"Wavelets at Imager" University of British Columbia

The Imager Wavelet Library, "wvlt", is a small library of wavelet-related functions in C that perform forward and inverse transforms and refinement. Support for 15 popular wavelet bases is included, with the ability to add more. The package also includes source for three shell-level programs to do wavelet processing on ASCII files and PPM images with some demo scripts. (The demos require "gnuplot" and "perl" to be installed on your system.) The code has been compiled and tested under various UNIX flavors (AIX, SunOS, IRIX, and HP-UX), DOS, and (partially) Macintosh and should port to other systems with few problems.
Imager Wavelets Software Library.

"Wavelet Image Compression Construction Kit" from Dartmouth

The Wavelet Image Compression Construction Kit is a set of free C++ source files for facilitating research in wavelet-based image compression. This code implements a wavelet transform-based image coder for grayscale images, and is designed to be a foundation upon which more more sophisticated coders can be built.
Wavelet Image Compression Construction Kit.

"AWFD" C++ class library

AWFD (Adaptivity, Wavelets & Finite Differences) C++ class library by the Department of Scientific Computing and Numerical Simulation at the University of Bonn is available for downloading. It is a C++ class library for wavelet/interpolet-based solvers for PDEs and integral equations. The main features of AWFD are: 1) Petrov-Galerkin discretizations of linear and non-linear elliptic and 2) parabolic PDE (scalar as well as systems) 3) Adaptive sparse grid strategy for a higher order interpolet multiscale basis 4) Adaptivity control via thresholding of wavelet coefficients 5) Multilevel lifting-preconditioner for linear systems 6) Dirichlet and Neumann boundary conditions.
"AWFD" C++ class library

"Wavelet" C++ class library by Martin Dietze

The "Wavelet" C++ class library includes classes and utility functions for images, Wavelet transforms, two-dimensional decompositions, image statistics and simple image manipulation. The Wavelet-transform code is based on Geoff Davis' well-known Wavelet Image Coding toolkit, but sacrifices some runtime performance for IMHO more flexible design. The code should compile with most recent C++ compilers. The library is available under the GPL.
Wavelet C++ class library by Martin Dietzey

Yale University

The Mathematics Department at Yale has made available wavelet software for de-noising, a wavelet packet library (written in C), and an educational package for X-windows.
Yale Wavelet Software.

Laboratory for Computational Vision Software at NYU

The The Laboratory for Computational Vision at NYU has made publicly available the following software packages: 1) Texture Analysis/Synthesis 2) EPWIC - Embedded Progressive Wavelet Image Coder. 3) matlabPyrTools - Matlab source code for multi-scale image processing, 4) The Steerable Pyramid, an (approximately) translation- and rotation-invariant multi-scale image decomposition, 5) Computational Models of cortical neurons, and 6) EPIC - Efficient Pyramid (Wavelet) Image Coder.
Laboratory for Computational Vision Software.

"MegaWave2" from CMLA of Ecole Normale Superieure de Cachan

MegaWave2 is a free software intended for image processing. It is made of 1) a C library of modules, that contains original algorithms written by researchers; and 2) a Unix/Linux package designed for the fast developpement of new image processing algorithms. The software is maintained and updated by Jacques Froment (kernel) and Lionel Moisan (modules) at CMLA (in Jean-Michel Morel's team), and benefits from the contribution of several other researchers. .
MegaWave2 Wavelet Software.

"Dataplore" by the Datan Software and Analysis GmbH.

Tool for Signal And TIme Series analysis, with graphical user interface. Contains standard facilities for signal processing as well as advanced features like wavelet techniques and methods of nonlinear dynamics. Systems: MS Windows, Linux, SUN Solaris 2.3, SGI Irix 5.3.
Dataplore by the Datan Software and Analysis GmbH.

"LabVIEW Advanced Signal Processing Add-on" from National Instruments

The LabVIEW add-on allows you to select an appropriate wavelet transform or to design one of your own through a graphical user interface to find the best wavelet or filter bank for your application. The wavelet and filter bank design tools apply to 1D signals and to 2D images. The toolset also includes wavelet analysis VIs, such as 1D and 2D analysis and synthesis filters, as well as many other useful functions for use in building custom LabVIEW applications.
LabVIEW Advanced Signal Processing Add-on.

"MR/1" from Multi Resolution Ltd

Multiresolution Analysis, for visualization, filtering, noise modeling, deconvolution, compression, vision modeling, image registering, feature detection, and much much more.
MR/1 Multiresolution Analysis Software.

"Wavelets Extension Pack" for Mathcad

Mathcad's Wavelet Extension Pack adds wavelet functions to Mathcad 8 Professional's built-in function library. It integrates over 60 wavelet functions including orthogonal and biorthogonal wavelet families such as Haar, Daubelts, Symmlets, Coiflets, and Bspline.
Wavelets Extension Pack for Mathcad.

"Wavestat" from Mabuse.de

WaveStat applies exploratory Cluster Analysis of picture data using wavelet-built coefficients. Cluster Analysis collects elements (i.e. pixels) of the same property (in this context this means: gray value) to a cluster. These clusters can be visualized by colorizing them or by reconstructing them to a grayscale picture.
Wavestat from Mabuse.de.

PV-Wave Signal Processing Toolkit ("SPT")

The Signal Processing Toolkit (SPT) is an add-on to PV-WAVE Advantage, almost entirely written in PV-WAVE with the source code supplied. The Toolkit concentrates on 1-D signal processing, with many of the functions extendable to 2-D for image processing, etc. simply by adding to the source code. In addition to the various functions which cover areas such as: models and analysis, filter approximation and realisation, transforms and spectrum analysis, statistical signal processing, optimisation and convenience routines for polynomial manipulation (of the transfer functions) and plotting functions, the wavelet part of the product computes the wavelet transform of a data sequence using compactly supported ortho-normal wavelets (using a quadrature mirror filters- QMF) Functions for computing and designing the QMF bank are supplied as well as a number of examples.
PV-Wave Signal Processing Toolkit.

"XploRe" by W. Haerdle

XploRe, developed by by W. Haerdle for data analysis, research and teaching, is promoted as a powerful tool for computational statistics. The package contains a number of wavelet processing tools. The main features are an extensive set of parametric and nonparametric methods incorporating many statistical modelling approaches, a high level object oriented programming language, an interactive graphic environment, a client/server architecture with a fully capable Java interface, an online help system, and a set of tutorials. XploRe contains a great variety of statistical methods that include: generalized linear models and generalized partial linear models, nonparametric methods such as kernel estimation and smoothing, spline smoothing, nonlinear time series analysis, modern regression techniques, and wavelets and neural networks. XploRe can be installed on single computers (PC or workstation), and in networks. XploRe runs on almost any platform.
XploRe.

W-Transform Matlab Toolbox

A toolbox to perform multiresolution analysis based on the W-transform is available. The W-transform is a class of discrete transforms that treats signal endpoints differently than usual and allows signals of any length to be handled efficiently. In addition to the toolbox (310 Kb tarred/compressed) there is a paper (590 Kb compressed PostScript) describing the W-transform and a manual (108 Kb compressed PostScript) for the toolbox.
W-Transform Matlab Toolbox by anon ftp.

"TimeStat" Wavelet Application

Windows program that performs FFT, wavelet transforms (many bases) in an Excel-like spreadsheet environment. You may want to download the extra file "tstat120.readme" at the following site too. In zip format.
TimeStat program.

2-D Wavelet Packet Analysis S+ Software by C. Jones

This 2-D Wavelet Packet analysis software determines the global fractal dimension of 2-D images. The software is used in research published in the paper: "2-D Wavelet Packet Analysis of Structural Self-Organization and Morphogenic Regulation in Filamentous Fungal Colonies." The entire paper is readable online and the full source code for S-Plus is provided in a link within the above paper.
Cameron Jones' 2-D WPA Software.

Brandon Whitcher's wavelet R, S+, and C code

On this page, you will find, in particular, "waveslim", which is his wavelet code accumulated over the years in S-plus converted into a package for R. He has recently included routines to handle three-dimensional data objects. Major features include: 1) Analysis of time series, images, 3D arrays using the DWT, MODWT, DWPT and MODWPT, 2) Standard wavelet thresholding techniques, 3) Wavelet analysis of covariance/correlation for bivariate time series, 4) Testing for homogeneity of variance in long memory processes, 5) Wavelet-based ML estimation for long memory processes, 6) Both standard (Donoho and Johnstone) and real data sets. Other libraries you will find at Whitcher's site is Rwave and C code performing DWTs and MODWTs.
Brandon Whitcher's wavelet R, S+, and C code.

Fourier-Wavelet Regularized Deconvolution ("ForWaRD") Software by Neelamani et al.

This software implements a fast hybrid deconvolution algorithm called Fourier-wavelet regularized deconvolution (ForWaRD) that comprises convolution system inversion followed by scalar shrinkage in both the Fourier domain and the wavelet domain. See the link for both the software and the paper that gives more details on this method.
Fourier-Wavelet Regularized Deconvolution (ForWaRD) Software.

"FAWAV" - A Fourier/Wavelet Analyzer by James Walker.

This FAWAV software goes with Walker's A Primer on Wavelets and their Scientific Applications. This programК does Fourier and wavelet analysis on digital signals (1D and 2D). It requires the Microsoft WINDOWS operating system..
FAWAV - A Fourier/Wavelet Analyzer by James Walker.

"WaveThresh" Software from the University of Bristol

Wavethresh is an add-on package, from the people in the Department of Mathematics at the University of Bristol, for the statistical package S-PLUS or freeware clone R. S-PLUS is based on the object-oriented S language developed at AT&T Bell Laboratories.
U of Bristol's WaveThresh Software.

"Wavelet Image Viewer" by Summus Ltd.

This is a commercial wavelet-based image compression plug-in for web browsers that claims to provide superior image quality, compression ratios, and speed. Visit their web page for a demo.
Wavelet Image Viewer Browser Plug-in.

"Matching Pursuit Video Codec" by Berkeley EE Researchers.

The Matching Pursuit Experimental Video Codec is based on the motion-transform hybrid video coding framework commonly employed in standard based system such as H.263 and MPEG2. Matching pursuit (MP) is an over-complete expansion technique that can be used in place of the DCT for prediction error coding after motion compensation. The objective of making this package freely available is to stimulate further research activities in the area of MP video coding.
Matching Pursuit Video Codec.

"AGU-Vallen Wavelet" by Vallen-Systeme GmbH and AGU.

AGU-Vallen Wavelet is a tool which allows to calculate and display the wavelet transform on individual waveforms.
AGU-Vallen Wavelet" by Vallen-Systeme GmbH and AGU.

"AutoSignal" by Systat

Autosignal performs complex signal analysis which includes FFT, autoregressions, moving averages, ARMA, exponential modeling, Minimum variance methods, eigen analysis, frequency estimation and wavelets.
AutoSignal by Systat.

"EPWIC" by Robert Buccigrossi and Eero Simoncelli.

EPWIC stands for Embedded Predictive Wavelet Image Coder, a grayscale image compression utility written in C.
EPWIC Wavelet Compressor.

"Wavelet Packet Laboratory for Windows" by Digital Diagnostics Corporation & Yale University.

The Wavelet Packet Laboratory for Windows is an interactive software tool for the Microsoft Windows operating environment that allows you to explore the properties of the Wavelet Packet and Local Trigonometric Transforms by performing adapted waveform analysis on digital signals. This package includes a users' manual and program PC diskette that allows hands-on signal analysis. Publisher/Price: AK Peters - 1994 3.5" Disk & Manual $300.00 (My guess is that this software is closely associated with M.V. Wickerhauser's wavelet packets research and his book: Adapted Wavelet Analysis from Theory to Software listed below in the Beginners Bibliography (AG).)
Wavelet Packet Laboratory.

"WSQ freeware" by Mladen Victor Wickerhauser.

Certified executables to perform the FBI's WSQ fingerprint image compression and decompression algorithm on 6 flavors of UNIX, Windows 98 and Windows 95. See Software for more of his software.
WSQ freeware by Wickerhauser.

Wavelet Transform Code by Paul Johnson

On this CD of biostatistical software, you will find code to calculate the power spectrum using the Marr and Morlet wavelet, with an application to examine tree growth variation. The CD includes a set of executable algorithms with instructions on their use, FORTRAN source code, and 3)a statistical analysis package.
Biostatistical Software by Paul Johnson.

"MIDAS" Astronomical Data Reduction Wavelet Transform

This is the online documentation from the "ESO-MIDAS User Guide Volume B: Data Reduction" for the Wavelet Transform functions built into the ESO-MIDAS software. ESO-MIDAS is the acronym for the European Southern Observatory - Munich Image Data Analysis System which is developed and maintained by the European Southern Observatory. The MIDAS system provides general tools for image processing and data reduction with emphasis on astronomical applications including imaging and special reduction packages for ESO instrumentation at La Silla.
"MIDAS" Detailed Documentation Describing Wavelet Transforms.

Видеоматериалы из Youtube.com

Mby-Sci — Sun, 08 Apr 2012 15:49:09 GMT