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.
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
3.2 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
