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Fourier Transform and Its Applications Using Microsoft EXCEL®

Shinil Cho


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.

About Editors

Shinil Cho attended Rikkyo University in Tokyo, Japan for his BS. He gained his MS from Seoul National University in Seoul, Korea and his PhD from The Ohio State University. Cho held post-doctoral fellowships at The Ohio State University and the University of Florida, and was a visiting professor at the University of South Carolina. He has been at La Roche College, where he is currently an Associate Professor, since 1995. Cho's current research interests include quantum computation, biometrics and physics education.

Table of Contents

Table of Contents
Chapter 1 The Principle of Superposition and the Fourier Series
1.1 The Principle of Superposition
1.2 Wave Equations
1.3 The Fourier Series
1.4 Orthonormal Basis

Chapter 2 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

Chapter 3 The Fourier Transform using EXCEL
3.1 Data Acquisition
3.2 Fourier Transform
3.3 The Effect of Windowing Function
3.4 Peak Peeking
3.5 2N-point FFT from N-point FFTs
3.6 Inverse Fourier Transform

Chapter 4 The Fourier Transforms in Physics
4.1 Examples of Acoustic Spectra and Data Analysis
4.2 Electronic Circuits
4.3 Telecommunication Signals
4.4 Spectroscopy (NMR and FT-IR)
4.5 Fourier Transforms in Optics
4.6 Quantum Mechanics

Chapter 5 Beyond the Fourier Transform Spectroscopy
5.1 Linear Prediction (LP) Method
5.2 Maximum Entropy (ME) Method
5.3 LPC Examples
5.4 LPC Cepstrum

A1. Notes on EXCEL
A2. Gibbs Phenomena
A3. Residual Theorem of Complex Integral
A4. Partial Integral Appeared in the Uncertainty Calculation
A5. Winer-Khintchine Theorem
A6. Levinson Algorithm



Paperback ISBN: 9780750329439

Ebook ISBN: 9781643272856

DOI: 10.1088/978-1-64327-286-3

Publisher: Morgan & Claypool Publishers


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