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This new edition of an indispensable text provides a clear
treatment of Fourier Series, Fourier Transforms, and FFTs. The
unique software, included with the book and newly updated for this
edition, allows the reader to generate, firsthand, images of all
aspects of Fourier analysis described in the text. Topics covered
include applications to vibrating strings, heat conduction, removal
of noise and frequency detection, filtering of Fourier Series and
improvement of convergence, and much more.
Mathematics and Music: Composition, Perception, and Performance,
Second Edition includes many new sections and more consistent
expectations of a student's experience. The new edition of this
popular text is more accessible for students with limited musical
backgrounds and only high school mathematics is required. The new
edition includes more illustrations than the previous one and the
added sections deal with the XronoMorph rhythm generator, musical
composition, and analyzing personal performance. The text teaches
the basics of reading music, explaining how various patterns in
music can be described with mathematics, providing mathematical
explanations for musical scales, harmony, and rhythm. The book
gives students a deeper appreciation showing how music is informed
by both its mathematical and aesthetic structures. Highlights of
the Second Edition: Now updated for more consistent expectations of
students' backgrounds More accessible for students with limited
musical backgrounds Full-color presentation Includes more thorough
coverage of spectrograms for analyzing recorded music Provides a
basic introduction to reading music Features new coverage of
building and evaluating rhythms
In the first edition of his seminal introduction to wavelets, James
S. Walker informed us that the potential applications for wavelets
were virtually unlimited. Since that time thousands of published
papers have proven him true, while also necessitating the creation
of a new edition of his bestselling primer. Updated and fully
revised to include the latest developments, this second edition of
A Primer on Wavelets and Their Scientific Applications guides
readers through the main ideas of wavelet analysis in order to
develop a thorough appreciation of wavelet applications.
Ingeniously relying on elementary algebra and just a smidgen of
calculus, Professor Walker demonstrates how the underlying ideas
behind wavelet analysis can be applied to solve significant
problems in audio and image processing, as well in biology and
medicine. Nearly twice as long as the original, this new edition
provides 104 worked examples and 222 exercises, constituting a
veritable book of review material Two sections on biorthogonal
wavelets A mini-course on image compression, including a tutorial
on arithmetic compression Extensive material on image denoising,
featuring a rarely covered technique for removing isolated,
randomly positioned clutter Concise yet complete coverage of the
fundamentals of time-frequency analysis, showcasing its application
to audio denoising, and musical theory and synthesis An
introduction to the multiresolution principle, a new mathematical
concept in musical theory Expanded suggestions for research
projects An enhanced list of references
Mathematics and Music: Composition, Perception, and Performance,
Second Edition includes many new sections and more consistent
expectations of a student's experience. The new edition of this
popular text is more accessible for students with limited musical
backgrounds and only high school mathematics is required. The new
edition includes more illustrations than the previous one and the
added sections deal with the XronoMorph rhythm generator, musical
composition, and analyzing personal performance. The text teaches
the basics of reading music, explaining how various patterns in
music can be described with mathematics, providing mathematical
explanations for musical scales, harmony, and rhythm. The book
gives students a deeper appreciation showing how music is informed
by both its mathematical and aesthetic structures. Highlights of
the Second Edition: Now updated for more consistent expectations of
students' backgrounds More accessible for students with limited
musical backgrounds Full-color presentation Includes more thorough
coverage of spectrograms for analyzing recorded music Provides a
basic introduction to reading music Features new coverage of
building and evaluating rhythms
In the first edition of his seminal introduction to wavelets, James
S. Walker informed us that the potential applications for wavelets
were virtually unlimited. Since that time thousands of published
papers have proven him true, while also necessitating the creation
of a new edition of his bestselling primer. Updated and fully
revised to include the latest developments, this second edition of
A Primer on Wavelets and Their Scientific Applications guides
readers through the main ideas of wavelet analysis in order to
develop a thorough appreciation of wavelet applications.
Ingeniously relying on elementary algebra and just a smidgen of
calculus, Professor Walker demonstrates how the underlying ideas
behind wavelet analysis can be applied to solve significant
problems in audio and image processing, as well in biology and
medicine. Nearly twice as long as the original, this new edition
provides * 104 worked examples and 222 exercises, constituting a
veritable book of review material * Two sections on biorthogonal
wavelets * A mini-course on image compression, including a tutorial
on arithmetic compression * Extensive material on image denoising,
featuring a rarely covered technique for removing isolated,
randomly positioned clutter * Concise yet complete coverage of the
fundamentals of time-frequency analysis, showcasing its application
to audio denoising, and musical theory and synthesis * An
introduction to the multiresolution principle, a new mathematical
concept in musical theory * Expanded suggestions for research
projects * An enhanced list of references * FAWAV: software
designed by the author, which allows readers to duplicate described
applications and experiment with other ideas. To keep the book
current, Professor Walker has created a supplementary website. This
online repository includes ready-to-download software, and sound
and image files, as well as access to many of the most important
papers in the field.
The Ising model provides a detailed mathematical description of
ferromagnetism and is widely used in statistical physics and
condensed matter physics. In this Student's Guide, the author
demystifies the mathematical framework of the Ising model and
provides students with a clear understanding of both its physical
significance, and how to apply it successfully in their
calculations. Key topics related to the Ising model are covered,
including exact solutions of both finite and infinite systems,
series expansions about high and low temperatures, mean-field
approximation methods, and renormalization-group calculations. The
book also incorporates plots, figures, and tables to highlight the
significance of the results. Designed as a supplementary resource
for undergraduate and graduate students, each chapter includes a
selection of exercises intended to reinforce and extend important
concepts, and solutions are also available for all exercises.
The Ising model provides a detailed mathematical description of
ferromagnetism and is widely used in statistical physics and
condensed matter physics. In this Student's Guide, the author
demystifies the mathematical framework of the Ising model and
provides students with a clear understanding of both its physical
significance, and how to apply it successfully in their
calculations. Key topics related to the Ising model are covered,
including exact solutions of both finite and infinite systems,
series expansions about high and low temperatures, mean-field
approximation methods, and renormalization-group calculations. The
book also incorporates plots, figures, and tables to highlight the
significance of the results. Designed as a supplementary resource
for undergraduate and graduate students, each chapter includes a
selection of exercises intended to reinforce and extend important
concepts, and solutions are also available for all exercises.
Fourier analysis is a mathematical technique for decomposing a
signal into identifiable components. It is used in the study of all
types of waves. This book explains the basic mathematical theory
and some of the principal applications of Fourier analysis, in
areas ranging from sound and vibration to optics and CAT scanning.
The author provides in-depth coverage of the techniques and
includes exercises that range from straightforward applications of
formulas to more complex collections of problems. The text will be
a valuable guide for courses in electrical engineering, applied
mathematics, and signal processing.
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