# Digital Fourier Analysis: Fundamentals

• Ken'iti Kido
Textbook

Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

1. Front Matter
Pages i-xiii
2. Ken’iti Kido
Pages 1-24
3. Ken’iti Kido
Pages 25-50
4. Ken’iti Kido
Pages 51-75
5. Ken’iti Kido
Pages 77-105
6. Ken’iti Kido
Pages 107-130
7. Ken’iti Kido
Pages 131-151
8. Ken’iti Kido
Pages 153-181
9. Back Matter
Pages 183-203

### Introduction

This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform.

Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations.  These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics.

For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader can test various cases and view the results until they fully understand the principle.

Additionally, the applet source code in Visual Basic is provided online, allowing this book to be used for teaching simple programming techniques.

A complete, intuitive guide to the basics, "Digital Fourier Analysis - Fundamentals" is an essential reference for undergraduate students in science and engineering.

### Keywords

Discrete Fourier Transform Fast Fourier Transform Fourier Transform Learning Tools Fourier Transform in Visual Basic Numerical Methods in Visual Basic Sine and Cosine Components Spectrum Analysis

#### Authors and affiliations

• Ken'iti Kido
• 1
1. 1.Yokohama-shiJapan

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4614-9260-3
• Copyright Information Springer Science+Business Media New York 2015
• Publisher Name Springer, New York, NY
• eBook Packages Physics and Astronomy
• Print ISBN 978-1-4614-9259-7
• Online ISBN 978-1-4614-9260-3
• Series Print ISSN 2192-4791
• Series Online ISSN 2192-4805
• Buy this book on publisher's site