Fourier transform and Its applications using Microsoft Excel / Shinil Cho.

Format:

Book

Author/Creator:

Cho, Shinil, author.

Series:

IOP Ebooks Series

Language:

English

Subjects (All):

Mathematical physics.

Transformations (Mathematics)--Data processing.

Transformations (Mathematics).

Physical Description:

1 online resource (189 pages)

Edition:

Second edition.

Place of Publication:

Bristol, England : IOP Publishing, [2023]

Summary:

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.

Contents:

Outline placeholder

Preface to the first edition

Preface to the second edition

Acknowledgements

Author biography

Shinil Cho

Chapter The principle of superposition and the Fourier series

1.1 The principle of superposition

1.2 One-dimensional standing wave

1.3 Fourier series

1.3.1 Fourier theorem

1.4 Orthonormal basis

1.5 Heat and diffusion equations

1.6 Two-dimensional standing wave and two-dimensional Fourier series

References

Chapter The Fourier transform

2.1 From the Fourier series to the Fourier transform

2.1.1 The concept of the Fourier transform

2.1.2 Mathematical properties of a Fourier transform

2.2 Practical computational issues of the Fourier transform

2.2.1 Sampling rate slower than signal frequency

2.2.2 Aliasing (folding noise)

2.2.3 A finite size sample

2.3 Discrete Fourier transform and fast Fourier transform

2.3.1 N-point FT from two (N/2)-point FTs

2.3.2 Algorithms of one- and two-dimensional FFTs

2.3.3 Energy spectrum and power spectrum

2.4 Linear response theory

2.4.1 Linear black box and frequency transfer function

2.4.2 Response to an arbitrary input function

2.4.3 Harmonic oscillator with external driving term

2.4.4 Dispersion relation

2.5 Cepstrum

Chapter 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 spectra

3.7.1 Human voice

3.7.2 Notes on vocal formant

3.7.3 Human voice when ill

3.7.4 Musical instruments

3.7.5 Cepstrum analysis

Chapter Applications of Fourier transform in physics

4.1 Electronic circuits.

4.1.1 CR-series circuit

4.1.2 RC-series circuit

4.1.3 LR-series circuit

4.1.4 RLC-series circuit

4.1.5 Note on filtering

4.2 Telecommunication signals

4.2.1 Amplitude modulation and demodulation

4.2.2 Frequency modulation and demodulation

4.3 Spectroscopy

4.3.1 Nuclear magnetic resonance spectroscopy

4.3.2 Pulse NMR

4.3.3 Fourier transform IR (FT-IR) spectroscopy

4.4 Optics

4.4.1 One-dimensional diffraction

4.4.2 Two-dimensional diffraction

4.4.3 Lens

4.4.4 Hologram

4.4.5 X-ray diffraction

4.5 Stochastic processes and Fourier transform

4.5.1 Characteristic function and central limit theorem

4.5.2 Brownian motion

4.5.3 Fluctuation-dissipation theorem in Brownian motion

4.5.4 Random frequency modulation and motional narrowing

4.6 Solving diffusion equation using Fourier transform

4.6.1 Diffusion equation

4.6.2 Green's function for wave equation

4.7 Quantum mechanics

4.7.1 Wave packet

4.7.2 Group velocity

4.7.3 Schrödinger equation with imaginary time

4.7.4 Heisenberg's uncertainty principle

4.7.5 Potential scattering-Born approximation

Chapter Quantum Fourier transforms

5.1 Quantum Fourier transform used by Shor's algorithm

5.1.1 Qbit

5.1.2 Quantum Fourier transform of N-qbit basis

5.1.3 Quantum Fourier transform of orthonormal basis

5.2 Quantum Fourier transform used in quantum walks

5.2.1 Quantum walk

5.2.2 Quantum Fourier transform for the quantum walk

Chapter Beyond the Fourier transform spectroscopy

6.1 LP method

6.1.1 Final prediction error

6.2 ME method

6.3 LPC examples

6.4 LPC cepstrum

Chapter

A1 Gibbs phenomena

A2 Cauchy's residual theorem of the complex integral

A3 Fourier transform of a step function U(ω).

A4 Explicit form of the impulse response of forced harmonic oscillator

A5 Hilbert transform and dispersion relation

A6 Derivation of dispersion relation χ′(ω) and χ′(ω)

A7 Winer-Khintchine theorem

A8 Proof of equation (4.112)

A9 Fourier transform of Gaussian function

A10 Fourier transform of exp(±λr)/r

A11 Partial integral in the uncertainty calculation

A12 Notes on EXCEL

A12.1 Autofill

A12.2 Adding 'data analysis'

A12.3 Enabling EXCEL macro

A13 Lists of VBA codes and EXCEL files for figures

A13.1 Fourier series of square pulse train

A13.2 Macro for rearranging terms

A13.3 Drawing 3D surface chart of z = f(x, y)

A13.4 VBA code and example of 1D-FFT

A13.5 VBA code and example of 2D-FFT

A13.6 VBA code of quantum walk

A13.7 Levinson algorithm

A13.8 Linear prediction coefficients and power spectrum

A13.9 Calculation of cepstrum coefficients from linear prediction method

References.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Includes bibliographical references.

ISBN:

9780750360463

0750360461

OCLC:

1429724464