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 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>>
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