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"Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of data--such as fingerprints, weather satellite photographs, and medical x-rays--that were previously thought to be impossible to condense without losing crucial details. This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient. The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets. The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose functions defined in a finite interval. Because of their interdisciplinary origins, wavelets appeal to scientists and engineers of many different backgrounds."

"Speech compression techniques based on traditional psychoacoustic model have been proposed by many researchers. We have suggested Discrete Wavelet Transform (DWT) supported by the same psychoacoustic model for speech compression. This paper presents a traditional psychoacoustic model to process equal partitions of total bandwidth spectrum of audio signal frequency to reduce redundancy by filtering out the tones and noise masker in speech signal. Here, the uniform filter banks are used for efficient computations and selection of appropriate threshold level for better compression of Discrete Wavelet Transformed coefficients. Daubechies wavelet filter bank is a nonlinear and asymmetric wavelet filter bank. It is equivalent to cochlear filter of human hearing system. The resemblance between Daubechies Filter Bank and our hearing system is used to develop the novel speech coder. Results have shown better performance in terms of compression factor (CF) and Signal-to-Noise Ratio (SNR) as compare to the methods suggested earlier."

"This update of the 1987 title of the same name is an examination of what is currently known about the probabilistic method, written by one of its principal developers. Based on the notes from Spencer's 1986 series of ten lectures, this new edition contains an additional lecture: The Janson Inequalities. These inequalities allow accurate approximation of extremely small probabilities. A new algorithmic approach to the Lovasz Local Lemma, attributed to Jozsef Beck, has been added to Lecture 8, as well. Throughout the monograph, Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favor of clearer exposition. The book is not encyclopedic--it contains only those examples that clearly display the methodology. The probabilistic method is a powerful tool in graph theory, combinatorics, and theoretical computer science. It allows one to prove the existence of objects with certain properties (e.g., colorings) by showing that an appropriately defined random object has positive probability of having those properties."

"This collection of independent case studies demonstrates how wavelet techniques have been used to solve open problems and develop insight into the nature of the systems under study. Each case begins with a description of the problem and points to the specific properties of wavelets and techniques used for determining a solution. The cases range from a very simple wavelet-based technique for reducing noise in laboratory data to complex work on two-dimensional geographical data display conducted at the Earthquake Research Institute in Japan. One case study shows how wavelet analysis is used in the development of a Japanese text-to-speech system for personal computers and another presents new wavelet techniques developed for and applied to the study of atmospheric wind, turbulent fluid, and seismic acceleration data. Although calculus and some junior and senior mathematics courses for scientists and engineers will suffice, a solid background in undergraduate mathematics, particularly analysis and numerical analysis, and some familiarity with the basics of wavelets are helpful for reading this book."

"This long-awaited update of Meyer's Wavelets: Algorithms & Applications includes completely new chapters on four topics: wavelets and the study of turbulence, wavelets and fractals (which includes an analysis of Riemann's nondifferentiable function), data compression, and wavelets in astronomy. The chapter on data compression was the original motivation for this revised edition, and it contains up-to-date information on the interplay between wavelets and nonlinear approximation. The other chapters have been rewritten with comments, references, historical notes, and new material. Four appendices have been added: a primer on filters, key results (with proofs) about the wavelet transform, a complete discussion of a counterexample to the Marr-Mallat conjecture on zero-crossings, and a brief introduction to Holder and Besov spaces."

"Wavelets adalah fungsi matematis yang memotong data menjadi komponen-komponen frekuensi yang berbeda, dimana fungsi ini "melihat" masing-masing komponen dengan suatu resolusi yang cocok dengan skalanya. Kelebihan wavelets dibandingkan dengan metoda Fourier konvensional adalah kemampuan yang sangat baik dalam menganalisa secara fisik terhadap sinyal yang memiliki diskontinuitas dan lonjakan-lonjakan tajam (sharp spikes). Para ahli telah mengembangkan wavelets secara independen daam bidang-bidang matematika, fisik kuantum, teknik elektro dan geologi seismik. Keterkatian bidang ilmu lain terhadap bidang ini selama sepuluh tahun terakhir memelopori aplikasi wavelet terbaru seperti kompresi citra, turbulensi, vii manusia (human vision) radar dan prediksi gempa bumi. Melalui dua bagian tulisan bagian pertama tulisan ini bertujuan untuk memperkenalkan wavelets secara mudah yang diawali dengan sejarahnya, metoda Fourier serta perbandingannya dengan wavelets aspek-aspek khusus wavelets. Pada bagian kedua akan dipaparkan beberapa aplikasi transformasi wavelet yang menarik seperti kompresi citra nada musik dan menghilangkan derau (de-noising). "