Jan 4, 2010

The Math Forum - Math Library - Fourier/Wavelets


  1. 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>>
  2. 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>>
  3. 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>>
  4. 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>>
  5. Wavelets - Salzburg, Austria
    An extensive list of links to Internet sources of information for wavelets, and some bibliographies. more>>
  6. 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>>

  All Sites - 118 items found, showing 1 to 50

  1. 1997 Linear Analysis Pages - Jonathan Borwein
    Mathematics 419, Linear Analysis (Simon Fraser University). Course information, assignments, extras for enrichment. Classical and applied analysis, special function theory, general analytic knowledge (cardinality, irrationality, complex analysis, continued ...more>>
  2. 1998 NSF-CBMS Regional Research Conferences in the Mathematical Sciences - Conference Board of the Mathematical Sciences (CBMS)
    A listing of (with links to) four conferences intended to stimulate interest and activity in mathematical research: Wavelet Analysis as a Tool for Computational and Harmonic Analysis; Blocks of Finite Reductive Groups, Deligne-Lustig Varieties, and Complex ...more>>
  3. Algebra with a Java- Applet - Jens-Uwe Dolinsky
    An Applet able to process symbolic and numeric simplifications of entered mathematical expressions, including symbolic differentiation, integration (standard integrals), and the development of Taylor as well as Fourier series. The .class files and a programming ...more>>
  4. Amara's Wavelet Page - Amara Graps
    Read a brief overview of wavelets, or listen to sounds compressed using wavelets. Page also includes an extensive list of wavelet resources. ...more>>
  5. Applied Wavelet Analysis Courses - Gerald Kaiser
    The Virginia Center for Signals and Waves, founded by mathematical physicist Gerald Kaiser, is dedicated to a physics-based approach to signal analysis and processing. Information about Kaiser's book A Friendly Guide to Wavelets, his curriculum vitae, ...more>>
  6. ATI's Mathematical & Physical Wavelets Course - Dr. Gerald Kaiser, Instructor
    Summary of an Applied Technology Institute Training Seminar in wavelet analysis (Applications to Generalized Radar and Sonar Analysis). ...more>>
  7. The Basics of MRI - Joseph P. Hornak; Rochester Institute of Technology
    An introduction to magnetic resonance imagining, which is based on the principles of nuclear magnetic resonance (NMR), a spectroscopic technique used by scientists to obtain microscopic chemical and physical information about molecules. See, in particular, ...more>>
  8. The Bath Wavelet Warehouse - Signal and Image Processing Group, Univ. of Bath, U.K.
    A collection of wavelet filters available for download. Biorthogonal Wavelets; Orthonormal Wavelets; References. ...more>>
  9. Bell Labs Wavelet Group - Bell Labs, Murray Hill, NJ
    Vivek Goyal, Jelena Kovacevic, Aleksandra Mojsilovic, Wim Sweldens. People, publications, applets (Fundamentals of Signal Decompositions, Series Expansions Using Wavelets and Modulated Bases Signal Compression and Subband Coding), other wavelet sites. ...more>>
  10. Bibliographies on Wavelets - Collection of Computer Science Bibliographies, University of Karlsruhe
    Search interface for an extensive collection of bibliographies on wavelets. ...more>>
  11. Books: Professional & Technical: Professional Science: Mathematics - Amazon.com
    Browse bestselling math books from the Professional and Technical Bookstore at Amazon.com, in such categories as Applied; Chaos & Systems; Geometry & Topology; Mathematical Analysis; Mathematical Physics; Number Systems; Pure Mathematics; Transformations; ...more>>
  12. Boost Your Skills With ATI Courses! - Applied Technology Institute (ATI)
    A center for technical training in the form of short courses and distance learning in space, communications, defense, sonar, radar, and signal processing. ...more>>
  13. Bytes of Science: An Internet Magazine - David S. Mazel, Ed.
    An Internet magazine on science and engineering, with tutorials and introductory articles on various areas of science, math, or engineering. Articles include: A Basis for Functions: The Fourier Series; The Fourier Transform: The Frequency in a Waveform; ...more>>
  14. Calculators On-Line Center: Part II - Mathematics - Martindale's Reference Desk
    Over 7,420 calculators for: Unit Conversion (Time, Distance, Length, Speed, Weight, etc.); Abacus; Basic Math; Complex Mathematics; Complex Math Education; Complex Math Calculators by Specialty: Algebra and Linear Algebra; Algorithms; Calculus; Central ...more>>
  15. Calculus (S.O.S. Mathematics) - Dept. of Mathematical Sciences, Univ. of Texas at El Paso
    An online course: learning units presented in worksheet format review the most important results, techniques and formulas in college and pre-college calculus. Logarithms and Exponential; Sequences; Series; Techniques of Integration; Local Behavior of ...more>>
  16. Center for Image Processing Research - Rensselaer Polytechnic Institute (RPI)
    Faculty, publications, research. See also the Center for Digital Video and Media Research(CDVMR), an NSF Industry/University Co-operative Research Center. ...more>>
  17. Center for the Mathematics of Waves - University of Delaware
    A summary of wave center reports, in zipped PostScript format downloads, from 1992 to 1997. Titles include Error Analysis in Numerical Solution of Acoustic Integral Equations, Multigrid Computation of Vector Potentials, Variational Methods for the Potential ...more>>
  18. CERFACS - European Centre for Research and Advanced Training in Scientific Computation
    CERFACS is one of the world's leading research institutes working on efficient algorithms for solving large-scale scientific problems. This involves the evaluation of existing, and the development of new tools which exploit high-performance serial, vector, ...more>>
  19. Compleat Sine Wave, Fourier Series - Bill Finzer, Key Curriculum Press
    Two "FPU Necessary [Geometer's] Sketches," one that illustrates Fourier series and another that draws a sine wave and lets you change the phase, amplitude, and frequency dynamically. ...more>>
  20. Connected Mathematics Project (CMP) - Michigan State University
    A project funded by the NSF to develop a complete mathematics curriculum for the middle grades (6-8), one rich in connections among the various topic strands of the subject, between mathematics and its applications in other disciplines, between the planned ...more>>
  21. Content-based Image Retrieval Project - Computer Science Department, Stanford University
    Project group members; online demos; SIMPLIcity: Semantics-sensitive Integrated Matching for Picture LIbraries; related links. ...more>>
  22. CSC Mathematical Topics - Center for Scientific Computing (CSC), Finland
    The Center provides support for research work requiring scientific computing. CSC offers WWW information services for a wide range of subjects, including software and publishing resources in chemistry, mathematics, molecular biology, physics, and visualizations ...more>>
  23. Daniel Lemire's homepage - Daniel Lemire
    Daniel Lemire is a researcher in wavelet theory, data thinning and subdivision schemes. Recently, he has been interested in applications of these mathematical tools to e-business and data mining. Site contains papers (downloadable, PDF format), software ...more>>
  24. Dartmouth College Wavelet Warriors - Math and Computer Science Depts., Dartmouth College, Hanover, NH
    People, research interests, projects, selected publications. ...more>>
  25. Dave Donoho - Statistics Dept., Stanford University
    Recent lectures ("Beyond Wavelets: A Case Study"); links to software and software the author has written or co-written. ...more>>
  26. The Department of Applied Science Wavelet Group - Lawrence Livermore National Laboratory
    The Wavelet Group is interested in studying the use of the wavelet transform in the solution of various types of problems. The primary area of current study is Signal Processing Using the Wavelet Transform Electrocardiogram (ECG). People, recent papers, ...more>>
  27. Differential Equations (S.O.S. Mathematics) - Dept. of Mathematical Sciences, Univ. of Texas at El Paso
    An online course: learning units presented in worksheet format review the most important results, techniques and formulas in college and pre-college differential equations. Sections include: Introduction and First Definitions; Modeling via Differential ...more>>
  28. Discovering Wavelets - Grand Valley State University (GVSU)
    Wavelets for undergraduates: a site designed to be a center of activity for incorporating wavelets into the undergraduate curriculum, with links to undergraduate projects based on wavelets and image compression, and to undergraduate research projects. ...more>>
  29. Discrete Fourier Series Transform - Eric Brasseur
    A brief introduction to the discrete Fourier transform and its application to signal sampling. Also available in French. ...more>>
  30. Drums That Sound Alike - Ivars Peterson (MathLand)
    Peterson writes that physicists and mathematicians have long recognized that the shape of the boundary enclosing a membrane plays a crucial role in determining the membrane's spectrum of normal-mode vibrations. He outlines the progress made on Mark Kac's ...more>>
  31. DSP First: A Multimedia Approach - McClellan, Schafter, & Yoder
    The CD-ROM portion of the book, containing, for each chapter: Demos - quicktime movies, sound files, etc. that help reinforce the concepts introduced in the text; Labs - MATLAB based laboratory exercises for in-depth study of certain concepts and ideas ...more>>
  32. Embedded TEX - David McCabe
    Mathematics typesetting for Word, Excel, other Microsoft Office programs, or any application that supports ActiveX. Download and install free trials. See also McCabe's tutorial, which explains the Fourier transform and Fourier series. ...more>>
  33. The Equal Tempered Scale and Some Peculiarities of Piano Tuning - Jim Campbell
    An article on tuning applications from the Precision Strobe Tuners site. The Phenomena of Sound and the Harmonic Series, with information about Fourier analysis; Beats; The Physics of Ringing Strings; The Evolution of the Equal Tempered Scale; Piano Tuning; ...more>>
  34. EZW Encoding - C. Valens
    An embedded zerotree wavelet (EZW) tutorial. Contents: Introduction; EZW encoding; The zerotree; How does it work?; The algorithm; Example; Coda; Notes; References. By the author of A Really Friendly Guide to Wavelets. ...more>>
  35. The Fast Lifting Wavelet Transform - C. Valens
    A tutorial on wavelet filters aimed at engineers. Focusses on "lifting," a technique for creating a general framework to design filters for every possible wavelet transform. May be read online or downloaded in PostScript format. ...more>>
  36. The FBI Fingerprint Compression Standard - Chris Brislawn
    A summary, with examples, of the Federal Bureau of Investigation's image coding standard for digitized fingerprints, developed and maintained by the FBI, Los Alamos National Lab, and the National Institute for Standards and Technology. The standard is ...more>>
  37. FFT Spectrum Analyser Demo applet - Iain Robin
    A Java applet that demonstrates the use of the Fast Fourier Transform (FFT) to determine the frequency spectrum of a discrete signal (time series). ...more>>
  38. FFTW - Matteo Frigo and Steven G. Johnson
    FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data. Download FFTW; read about its features; subscribe to its mailing list for announcements. ...more>>
  39. Fourier Synthesis - Manfred Thole
    A periodic signal can be described by a Fourier decomposition as a Fourier series, i.e. as a sum of sinusoidal and cosinusoidal oscillations. By reversing this procedure a periodic signal can be generated by superimposing sinusoidal and cosinusoidal waves. ...more>>
  40. Fractal Seeks Wavelet - Henri Tourneur; De Montfort University
    A research project exploring links between fractals and wavelets for 1D-Signals. With results and references. Results include: The Kohonen Neural Network (many images); Self-affine Cartoons... Mandelbrot; Is Bach music fractal?; Fractal processing snapshots ...more>>
  41. Free Software which You Can Download - Will Naylor
    Download WNLIB, an ANSCII-C subroutine library which includes numerical routines, data structures, random number generators, and more. ...more>>
  42. Gamelan - The Official Java Directory - EarthWeb, Inc.
    Gamelan's primary mission is to serve as a central registry and directory of Java resources. Much like Yahoo!, Gamelan collects links to resources stored on other sites across the Web. However, unlike Yahoo!, Gamelan's mission is specific - Gamelan collects ...more>>
  43. Gilbert Strang - Dept. of Mathematics, Massachusetts Institute of Technology (MIT)
    Books and publications, including recent wavelet papers. ...more>>
  44. Guide to Wavelet Sources - Steve Baum; Dept of Oceanography, Texas A&M University
    A 1996 site with links to tutorials, software reviews, and other wavelet sites. [Compressed using gzip so cannot be rendered by all browsers.] ...more>>
  45. Homepage & Papers - Dr. Peter Singer
    Dr. Singer is associated with the MeVis-Center for Diagnostic Systems and Medical Visualization at the Univ. of Bremen, Germany. His interests and publications include: mathematics of finance; Fourier analysis; fractals; medical image processing; stochastic ...more>>
  46. IDL Wavelet Workbench - Amara Graps
    A library or "toolkit" written in the IDL language that demonstrates wavelet concepts as well as providing wavelet functions to manipulate data. This library can be run from a graphical user interface, or it can be called from the IDL command level. ...more>>
  47. Image Coding Using Wavelets - Signal and Image Processing Group, University of Bath
    Read the article "What makes a good orthonormal wavelet for image compression?" Download other wavelet articles in PDF or PostScript format. Visit the Wavelet Warehouse, a repository of wavelet filters (biorthogonal and orthonormal) to download and ...more>>
  48. Image Compression - from DCT to Wavelets: A Review - Subhasis Saha
    An article published in ACM Crossroads, the student magazine of the Association for Computing Machinery, about how recent growth in data-intensive multimedia-based Web applications has not only sustained the need for more efficient ways to encode signals ...more>>
  49. Interactive Mathematics - Murray Bourne, Ngee Ann Polytechnic, Singapore
    Flash Tutorials for Pre-Calculus (Algebra, Trigonometry, Logarithms, Complex Number Systems, Graphs); Calculus (Differentiation - The Derivative, its Applications, Deriving Transcendental Functions; Integration, its Applications and Methods), and Advanced ...more>>
  50. Interference of Sinusoidal Waveforms - Konstantin Lukin
    A Java applet that demonstrates the sum of two waves with variable wavelength, amplitude, and phase. Includes source code. ...more>>

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