Fourier transform and Its applications using Microsoft Excel /

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"Version: 20231101"--Title page verso.Includes bibliographical references.part 1. Foundation and Hands-on experiment of Fourier transform. 1. The principle of superposition and the Fourier series -- 1.1. The principle of superposition -- 1.2. One-dimensional standing wave -- 1.3. Fourier series -- 1.4. Orthonormal basis -- 1.5. Heat and diffusion equations -- 1.6. Two-dimensional standing wave and two-dimensional Fourier series2. The Fourier transform -- 2.1. From the Fourier series to the Fourier transform -- 2.2. Practical computational issues of the Fourier transform -- 2.3. Discrete Fourier transform and fast Fourier transform -- 2.4. Linear response theory -- 2.5. Cepstrum3. Hands-on Fourier transform using EXCEL? -- 3.1. Data acquisition -- 3.2. Computational steps to perform EXCEL's Fourier transform -- 3.3. The effect of the windowing function -- 3.4. Peak peeking -- 3.5. Demonstration of N-point FFT from two (N/2)-point FFTs -- 3.6. Inverse Fourier transform -- 3.7. Acoustic spectrapart 2. Advanced theories and topics on Fourier transform. 4. Applications of Fourier transform in physics -- 4.1. Electronic circuits -- 4.2. Telecommunication signals -- 4.3. Spectroscopy -- 4.4. Optics -- 4.5. Stochastic processes and Fourier transform -- 4.6. Solving diffusion equation using Fourier transform -- 4.7. Quantum mechanics5. Quantum Fourier transforms -- 5.1. Quantum Fourier transform used by Shor's algorithm -- 5.2. Quantum Fourier transform used in quantum walks6. Beyond the Fourier transform spectroscopy -- 6.1. LP method -- 6.2. ME method -- 6.3. LPC examples -- 6.4. LPC cepstrum.This book demonstrates Microsoft EXCEL?-based Fourier transform of selected physics examples, as well as describing spectral density of the auto-regression process in relation to Fourier transform. Rather than offering rigorous mathematics, the book provides readers with an opportunity to gain an understanding of Fourier transform through the examples. They will acquire and analyze their own data following the step-by-step procedure outlined, and a hands-on acoustic spectral analysis is suggested as the ideal long-term student project. This new edition updates and greatly expands upon the first, with additional examples and exercises in various application domains as well as a new chapter on Quantum random walks and Fourier analysis.Professional and scholarly.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Shinil Cho attended Rikkyo University in Tokyo, Japan, for his BS degree; Seoul National University in Seoul, Korea, for his MS; and the Ohio State University in Ohio, USA, for his PhD. He held post-doctoral fellowships at the Ohio State University and University of Florida, and he was also a visiting professor at University of South Carolina. He has been at La Roche University since 1995. Currently he is a professor at La Roche. He has conducted research in cryogenic magnetic resonance spectroscopy below 1 K and biometric fingerprint authentication. His current research interest includes quantum computation, biometrics, and physics education. Other than physics, he has many publications and has done many presentations on biometrics in London, Gothenburg, Tokyo, Hongkong, Singapore, and several cities in the United States.Title from PDF title page (viewed on January 4, 2024).

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Publisher

: .,

Collation

1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9780750360449

Classification

515/.723

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-

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Edition

Second edition.

Subject(s)

SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.
Fourier transformations
Transformations (Mathematics)

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Statement of Responsibility

Shinil Cho.

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