Fourier Analysis and Integral Transformations with Applications in Engineering

The present book entitled "Fourier Analysis and Integral Transforms with Applications in Engineering" intends to be a useful tool mainly for students enrolled in a technical university, both in bachelor and master degree programs, but also to engineers involved in research.

The content is structured in four chapters and annexes, each chapter presenting definitions, properties, examples, and focusing on partially or solved exercises. If an exercise is not explicitly solved, then it contains hints and the final answer. An important part of the book is represented by various applications in engineering together with numerous MATLAB and Maple examples. All is meant to facilitate a good understanding of the theoretical notions.

Fourier Analysis and Integral Transformations with Applications in

Engineering

Chapter 1. Fourier Analysis

1.1 The pre-Hilbert space R

1.2 Generalized Fourier Series

1.3 Trigonometric Fourier Series

1.4 Convergence of the Fourier Series

1.5 Fourier Series of Even and Odd Functions

1.6 Complex Fourier Series

1.7 Signal Fourier Series Representation

1.8 Exercises

1.9 MATLAB Applications

1.10 Maple Applications

Chapter 2. Fourier Transform

2.1 Definition

2.2 Properties of the Fourier Transform

2.3 The Inversion Formula

2.4 Fourier Integral

2.5 Discrete Fourier Transform (DFT)

2.6 Fast Fourier Transform (FFT)

2.7 Exercises

2.8 MATLAB Applications

2.9 Maple Applications

Chapter 3. Laplace Transform

3.1 Definition

3.2 Properties of the Laplace Transform

3.3 Inverse Laplace Transform

3.4 Applications of the Laplace Transform

3.5 Exercises

3.6 MATLAB Applications

3.7 Maple Applications

Chapter 4. Z Transform

4.1 Definition

4.2 Properties of the Z Transform

4.3 Determination of the Original

4.4 Applications of the Z Transform

4.5 Exercises

4.6 MATLAB Applications

4.7 Maple Applications

A Tables of Integral Transforms

A.1 Fourier Transform

A.2 Cosine Fourier Transform

A.3 Sine Fourier Transform

A.4 Laplace Transform

A.5 Z Transform

Bibliography