The Evolution of Applied Harmonic Analysis : Models of the Real World

"...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied." — R.N. Bracewell, Stanford University A sweeping exploration of essential concepts and applications in modern mathematics and science through the unifying framework of Fourier analysis! This unique, extensively illustrated book describes the evolution of harmonic analysis, integrating theory and applications in a way that requires only some general mathematical sophistication and knowledge of calculus in certain sections. Key features: Historical sections interwoven with key scientific developments showing how, when, where, and why harmonic analysis evolved Exposition driven by more than 150 illustrations and numerous examples Concrete applications of harmonic analysis to signal processing, computerized music, Fourier optics, radio astronomy, crystallography, CT scanning, nuclear magnetic resonance imaging and spectroscopy Includes a great deal of material not found elsewhere in harmonic analysis books Accessible to specialists and non-specialists "The Evolution of Applied Harmonic Analysis" will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, and mathematics. Content Level » Graduate Keywords » Harmonic analysis - fourier analysis - signal processing

…can Be Thoroughly Recommended To Any Reader Who Is Curious About The Physical World And The Intellectual Underpinnings That Have Lead To Our Expanding Understanding Of Our Physical Environment And To Our Halting Steps To Control It. Everyone Who Uses Instruments That Are Based On Harmonic Analysis Will Benefit From The Clear Verbal Descriptions That Are Supplied.

— R.n. Bracewell, Stanford University

a Sweeping Exploration Of Essential Concepts And Applications In Modern Mathematics And Science Through The Unifying Framework Of Fourier Analysis! This Unique, Extensively Illustrated Book Describes The Evolution Of Harmonic Analysis, Integrating Theory And Applications In A Way That Requires Only Some General Mathematical Sophistication And Knowledge Of Calculus In Certain Sections.

key Features:

* Historical Sections Interwoven With Key Scientific Developments Showing How, When, Where, And Why Harmonic Analysis Evolved

* Exposition Driven By More Than 150 Illustrations And Numerous Examples

* Concrete Applications Of Harmonic Analysis To Signal Processing, Computerized Music, Fourier Optics, Radio Astronomy, Crystallography, Ct Scanning, Nuclear Magnetic Resonance Imaging And Spectroscopy

* Includes A Great Deal Of Material Not Found Elsewhere In Harmonic Analysis Books

* Accessible To Specialists And Non-specialists

the Evolution Of Applied Harmonic Analysis Will Engage Graduate And Advanced Undergraduate Students, Researchers, And Practitioners In The Physical And Life Sciences, Engineering, And Mathematics.

" ... can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied."--R.N. Bracewell, Stanford University A sweeping exploration of essential concepts and applications in modern mathematics and science through the unifying framework of Fourier analysis! This unique, extensively illustrated book describes the evolution of harmonic analysis, integrating theory and applications in a way that requires only some general mathematical sophistication and knowledge of calculus in certain sections. Key features: * Historical sections interwoven with key scientific developments showing how, when, where, and why harmonic analysis evolved * Exposition driven by more than 150 illustrations and numerous examples * Concrete applications of harmonic analysis to signal processing, computerized music, Fourier optics, radio astronomy, crystallography, CT scanning, nuclear magnetic resonance imaging and spectroscopy * Includes a great deal of material not found elsewhere in harmonic analysis books * Accessible to specialists and non-specialists "The Evolution of Applied Harmonic Analysis" will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, and mathematics A sweeping exploration of essential concepts and applications in modern mathematics and science through the unifying framework of Fourier analysis! This unique, extensively illustrated book, accessible to specialists and non-specialists, describes the evolution of harmonic analysis, integrating theory and applications in a way that requires only some general mathematical sophistication and knowledge of calculus in certain sections. Historical sections interwoven with key scientific developments show how, when, where, and why harmonic analysis evolved "The Evolution of Applied Harmonic Analysis" will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, and mathematics. Front Matter....Pages i-xxi Joseph Fourier: The Man and the Mathematician....Pages 1-29 Introduction to Harmonic Analysis....Pages 31-63 Telecommunications and Space Exploration....Pages 65-112 Sound, Music, and Computers....Pages 113-142 Fourier Optics and the Synchrotron Light....Pages 143-177 X-ray Crystallography: Protein Structure and DNA....Pages 179-213 The Radon Transform and Computerized Tomography....Pages 215-236 Nuclear Magnetic Resonance: Imaging and Spectroscopy....Pages 237-274 Radioastronomy and Modern Cosmology....Pages 275-310 Back Matter....Pages 311-351 "The Evolution of Applied Harmonic Analysis will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, and mathematics."--BOOK JACKET Orphaned when still a child, Joseph Fourier went through the French Revolution, the Napoleonic era, and the following Restoration as a high ranking public servant.