内容説明
信号解析，スペクトル解析，高速フーリエ変換，制御工学，線形システム理論を学ぶ基礎として必須であるフーリエ解析を簡単な英文で解説する。重要語には日本語を併記し，解析で使用するMATLABのコードも紹介。
目次
1．Overview of Fourier Analysis
1.1 History of Fourier Analysis
1.2 Illustrative Examples
1.2.1 Shape of Sound
1.2.2 Image Processing
1.2.3 Health Monitoring of Railroad Tracks
1.2.4 Structural Control
1.3 Key Points of Fourier Analysis
Problems
2．Mathematical Fundamentals for Fourier Analysis
2.1 Complex Number
2.2 Differential and Integral Calculus
2.2.1 Differential Calculus
2.2.2 Indefinite and Definite Integral Calculus
2.3 Partial Derivatives
2.4 Exponential and Logarithmic Functions
2.5 Trigonometric Functions
2.6 Various Functions
2.6.1 Hyperbolic Functions
2.6.2 Heaviside Step Function
2.6.3 Dirac Delta Function
Problems
3．Fourier Series
3.1 Periodic Phenomena
3.2 Expression of a Periodic Function
3.3 Complex Form of Fourier Series
Problems
4．Fourier Transform
4.1 Definition of Fourier Transform
4.2 Properties of Fourier Transform
4.3 Spectrum, Energy Spectral Density, and Correlation Function
4.4 Fourier Transforms of Special Functions
Problems
5．Signal Sampling and Reconstruction
5.1 The Sampling Theorem
5.2 Selection of Sampling Period
5.3 Reconstruction of Signal from Its Samples
Problems
6．Discrete Fourier Transform and Fast Fourier Transform
6.1 Discrete Fourier Transform
6.2 Fast Fourier Transform
Problems
7．Applications to Engineering Problems
7.1 Analysis of Sound
7.2 Analysis of Seismic Wave
7.3 Processing of Surface Electromyography (sEMG)
Problems
8．Application to Mathematical Problems in Engineering
8.1 Linear System and Impulse Response
8.2 Partial Differential Equation
Problems
9．Multi-Dimensional Fourier Transform
9.1 Definition of Multi-Dimensional Fourier Transform
9.2 Application to Image Compression
9.3 Application to Computerized Tomography
Problems
10．Laplace Transform
10.1 Definition of Laplace Transform
10.2 Frequency Response
10.3 Comparison of Fourier and Laplace Transforms
Problems
Appendix
References
Answers to Problems
Index
